Halacha

הלכה א
פֵּרוֹת שֶׁחֶזְקָתָן מִן הַהֶפִקִר. כְּגוֹן הַשִּׁיתִין וְהָרִימִין וְהָעוֹזְרָדִין וּבְנוֹת שׁוּחַ וּבְנוֹת שִׁקְמָה וְהַגּוּפָנִין וְנוֹבְלוֹת תְּמָרָה וְהֵן שֶׁעֲדַיִן לֹא הִטִּילוּ שְׂאוֹר הַנִּצְפָּה וְהַכֻּסְבַּר וְכַיּוֹצֵא בָּהֶן. פְּטוּרִין מִן הַדְּמַאי. וְהַלּוֹקְחָן מֵעַם הָאָרֶץ אֵינוֹ צָרִיךְ לְהַפְרִישׁ מֵהֶן תְּרוּמַת מַעֲשֵׂר וְלֹא מַעֲשֵׂר שֵׁנִי מִפְּנֵי שֶׁחֶזְקָתָן מִן הַהֶפְקֵר. אֲפִלּוּ אָמַר לוֹ עַם הָאָרֶץ אֵינָם מְעֻשָּׂרִין הֲרֵי אֵלּוּ פְּטוּרִין מִן הַמַּעַשְׂרוֹת עַד שֶׁיִּוָּדַע לוֹ שֶׁהֵן מִן הַשָּׁמוּר:
כסף משנה
1.
Fruits that we can assume to be ownerless:1That grow wild and do not have an owner. Such produce does not have to be tithed. e.g., wild figs,2Our definition of this and the following terms are dependent on the definitions given in the Rambam's Commentary to the Mishnah (Demai 1:1) as interpreted by Rav Kapach. brush berries, thorn apples, white figs, other species of wild figs, anise, dates that fall of the tree before they have swelled,3The literal translation is "when they will become yeast," the intent is when they will swell like bread into which yeast was placed. See the Rambam's Commentary to the Mishnah (Ma'aserot 1:2). capers, coriander, and the like are free from the stringency of demai. One who purchases them from a common person does not have to separate terumat ma'aser or the second tithe from them for we assume that they grew ownerless. Even if a common person told him that they have not been tithed, they are exempt from the tithes until it is known that they grew from produce that was guarded.4In which instance even if generally, the species is exempt, in this instance, the produce must be tithed.

הלכה ב
הַבְּכוֹרוֹת וְהַסְּיָּיפוֹת שֶׁבְּבִקְעָה פְּטוּרִין מִן הַדְּמַאי. וְשֶׁבְּגִנָּה חַיָּבִין מִפְּנֵי שֶׁהֵן נִשְׁמָרִין. וְאֵלּוּ הֵן הַבְּכוֹרוֹת. כָּל הַפֵּרוֹת שֶׁבִּכְּרוּ עַד שֶׁלֹּא הוֹשִׁיבוּ שׁוֹמֵר עַל הַבִּקְעָה לִשְׁמֹר פֵּרוֹתֶיהָ. וְהַסְּיָּיפוֹת הֵן הַפֵּרוֹת שֶׁיִּשָּׁאֲרוּ אַחַר שְׁיְּקַפְּלוּ הַמִּקְצוֹעוֹת שֶׁבַּשָּׂדוֹת וְיַנִּיחוּם בְּלֹא שׁוֹמֵר. וְכֵן הַחֹמֶץ הֶעָשׂוּי מִן הַתְּמָדִים פָּטוּר מִן הַדְּמַאי:
כסף משנה
2.
Produce that ripens first and last in a valley are exempt from the obligations of demai.5The owners generally leave such produce free to be taken by anyone, as the Rambam proceeds to explain. Hence, there is no obligation to separate tithes from it. Similar produce in a garden is liable, because it is watched.
What is meant by produce that ripens first? All the produce that ripens before [the owner] employs a guard for the valley to protect his produce.
What is meant by produce that ripens last? The produce that remains after the reapers have folded away their nets6The nets where grapes and figs that have been harvested are kept to dry [ibid. (Nedarim 8:4)]. in the field and left them without a guard. Similarly, vinegar made from wine dregs7The peels and seeds of the grapes and the dregs that are separated from the wine and fall to the bottom of the container [ibid. (Ma'aserot 5:6)].
Our translation follows the standard printed text of the Mishneh Torah. There are manuscripts and early printings that stated tamarim instead of temadim. According to that version, the translation would be "date vinegar." The Radbaz and the Kessef Mishneh, however, follow the version stated in the standard texts.
is exempt from the obligations of demai.8The Kessef Mishnehexplains that the rationale is that the wine dregs are usually left as ownerless. Hence, it is only in a place where that is the common practice that this law applies.

הלכה ג
כְּשֶׁגָּזְרוּ עַל הַדְּמַאי לֹא גָּזְרוּ אֶלָּא עַל פֵּרוֹת הָאָרֶץ שֶׁהֶחֱזִיקוּ בָּהּ עוֹלֵי בָּבֶל בִּלְבַד שֶׁהוּא מִכְּזִיב וְלִפְנִים וּכְזִיב עַצְמָהּ כְּלַחוּץ. וְכָל הַפֵּרוֹת הַנִּמְצָאוֹת מִכְּזִיב וְלַחוּץ פְּטוּרִין מִן הַדְּמַאי שֶׁחֶזְקָתָן מִפֵּרוֹת מָקוֹם שֶׁנִּמְצְאוּ בּוֹ:
כסף משנה
3.
When decrees were enacted concerning demai, they were enacted only with regard to produce from the land that was inhabited by the Jews who returned from Babylonia,9In contrast to the area inhabited by the Jews who ascended from Egypt in the first conquest. i.e., from Kziv inward.10See Hilchot Terumah, ch. 1, for a description of these geographic terms. Kziv itself is considered as outside these boundaries. All produce from Kziv and further are exempt from the obligations of demai for we operate under the assumption that the produce came from the place where it is found.11Conversely, we operate under the assumption that any produce found within the borders of Eretz Yisrael is bound by the restrictions of demai [the Rambam's Commentary to the Mishnah (Demai 1:3)].

הלכה ד
פֵּרוֹת שֶׁיָּדוּעַ שֶׁהֵן מִפֵּרוֹת הָאָרֶץ שֶׁהֶחֱזִיקוּ בָּהּ עוֹלֵי בָּבֶל אַף עַל פִּי שֶׁהֵן נִמְצָאוֹת בְּסוּרְיָא וְאֵין צָרִיךְ לוֹמַר בָּאָרֶץ שֶׁהֶחֱזִיקוּ בָּהּ עוֹלֵי מִצְרַיִם בִּלְבַד הֲרֵי אֵלּוּ חַיָּבִין בִּדְמַאי. וּמַפְרִישִׁין מֵהֶן תְּרוּמַת מַעֲשֵׂר וּמַעֲשֵׂר שֵׁנִי. לְפִיכָךְ הַדְּבֵלָה הַשְּׁמֵנָה שֶׁאֵין כְּמוֹתָהּ אֶלָּא בָּאָרֶץ שֶׁהֶחֱזִיקוּ עוֹלֵי בָּבֶל וְכֵן הַתְּמָרִים הַגְּדוֹלִים וְהֶחָרוּבִין הַשָּׁוִים וְהָאֹרֶז הַלָּבָן בְּיוֹתֵר וְהַכַּמּוֹן הַגָּדוֹל מִתְעַשְּׂרִין דְּמַאי בְּכָל אֶרֶץ יִשְׂרָאֵל וּבְסוּרְיָא. וְכֵן כָּל כַּיּוֹצֵא בְּפֵרוֹת אֵלּוּ:
כסף משנה
4.
When we know12If, however, there is a doubt concerning the matter, we assume that the produce grew in the land where it was found. that produce was grown in the land that was inhabited by the Jews who ascended from Babylonia, the laws of demai apply with regard to it even though it is presently found in Syria or in the land that was inhabited only by the Jews who ascended from Egypt. [Thus] terumat ma'aser and the second tithe must be separated from it.
Therefore a fat fig whose species is found only in the land inhabited by the Jews who ascended from Babylon - and similarly, large dates, straight carobs,13Our translation is taken from the Rambam's Commentary to the Mishnah (Demai 2:1). rice that is exceedingly white, and oversized cumin14All of these species grow only in Eretz Yisrael. - must be tithed like demai in the entirety of Eretz Yisrael and in Syria. Similar laws apply with regard to all produce that is comparable to these species.

הלכה ה
הַחַמָּרִים שֶׁהֵבִיאוּ פֵּרוֹת לְצוֹר חַיָּבִין בִּדְמַאי שֶׁחֶזְקָתָן מֵהָאָרֶץ שֶׁהֶחֱזִיקוּ עוֹלֵי בָּבֶל שֶׁהִיא הַקְּרוֹבָה לָהּ. וְהָאֹרֶז אֵין חוֹשְׁשִׁין לוֹ אֶלָּא כָּל הָאֹרֶז הַנִּמְצָא חוּצָה לָאָרֶץ שֶׁהִיא קְרוֹבָה לָאָרֶץ שֶׁהֶחֱזִיקוּ עוֹלֵי בָּבֶל פָּטוּר מִן הַדְּמַאי אֶלָּא אִם כֵּן הָיָה נִכָּר כְּמוֹ שֶׁבֵּאַרְנוּ:
כסף משנה
5.
When donkey-drivers bring produce to Tyre,15A city in Southern Lebanon, close to, but not immediately bordering on Eretz Yisrael. the laws governing demai apply to it, for we assume that it came from the nearby land inhabited by the Jews who ascended from Babylonia.16Since the produce was brought by donkey-drivers who travel longer distances, we consider the possibility that it was brought from Eretz Yisrael (Radbaz). As indicated by a comparison to the following halachah, here we are speaking about a caravan of donkeys. We do not harbor any suspicions with regard to rice. Instead, all the rice that is found in the Diaspora that neighbors the land which was inhabited by the Jews who ascended from Babylonia is exempt17Because rice which requires plentiful water is not usually grown in Eretz Yisrael. from demai unless it was obvious that it grew [only in Eretz Yisrael] as we explained.18As explained in the previous halachah.

הלכה ו
הַלּוֹקֵחַ מִבַּעֲלֵי אוֹצָרוֹת בְּצוֹר פָּטוּר מִן הַדְּמַאי וְאֵין אוֹמְרִין שֶׁמָּא מִפֵּרוֹת הָאָרֶץ אֲצָרוֹ. וְכֵן חֲמוֹר יְחִידִי שֶׁנִּכְנַס לְצוֹר וְהוּא טָעוּן פֵּרוֹת פָּטוּר מִן הַדְּמַאי שֶׁחֶזְקָתָן מִשְּׂדֵה הָעִיר:
כסף משנה
6.
When a person purchases [produce] from the owners of storehouses in Tyre, he is exempt from [the obligations of] demai. We do not say that they stored produce from Eretz Yisrael.19But instead, stored the local produce. Similarly, if one donkey20As opposed to the caravan mentioned in the previous halachah, a single donkey-driver will travel short distances. enters Tyre laden with produce, it is exempt from [the obligations of] demai, for we assume that [the produce comes] from the fields around the city.

הלכה ז
הַלּוֹקֵחַ מִבַּעֲלֵי אוֹצָר בְּצִידוֹן חַיָּב בִּדְמַאי מִפְּנֵי שֶׁקְּרוֹבָה הִיא יוֹתֵר מִצּוֹר שֶׁחֶזְקָתָהּ שֶׁאוֹצְרִין מִפֵּרוֹת הָאָרֶץ שֶׁהֶחֱזִיקוּ עוֹלֵי בָּבֶל. אֲבָל הַלּוֹקֵחַ מִן הַחַמָּרִים בְּצִידוֹן פָּטוּר מִן הַדְּמַאי מִפְּנֵי שֶׁחֶזְקָתָן שֶׁמְּבִיאִין מִחוּצָה לָאָרֶץ:
כסף משנה
7.
When a person purchases [produce] from the owners of storehouses in Tzidon,21Also a city in Southern Lebanon. It is very close to Eretz Yisrael.
The commentaries have questioned the Rambam's comments, noting that in actual fact, Tyre is closer to Eretz Yisrael than Tzidon. Among the explanations given is that there were two cities named Tzidon and the smaller one was in fact closer to Eretz Yisrael than Tyre. See Rambam LeAm.
he is obligated in [the laws of] demai, because it is closer to Eretz Yisrael than Tyre and we operate under the assumption that they store produce from the land inhabited by the Jews who ascended from Babylonia. If, however, one purchases [produce] from donkey-drivers in Tzidon, it is exempt from [the obligations of] demai, for we assume that they are bringing [the produce] from the Diaspora.22Here as well we are speaking about a caravan of donkey-drivers who travel long distances. As such, it is unlikely that they brought produce from Eretz Yisrael, for it is relatively close.

הלכה ח
הַלּוֹקֵחַ מִן הָעַכּוּ''ם בָּאָרֶץ שֶׁהֶחֱזִיקוּ עוֹלֵי בָּבֶל אִם הָיָה תַּגָּר עַכּוּ''ם שֶׁלּוֹקֵחַ מִיִּשְׂרָאֵל הֲרֵי פֵּרוֹתָיו דְּמַאי. לְפִיכָךְ בָּרִאשׁוֹנָה בִּזְמַן שֶׁהָיָה רֹב אֶרֶץ יִשְׂרָאֵל בְּיַד יִשְׂרָאֵל הַלּוֹקֵחַ מִכָּל תַּגָּר עַכּוּ''ם מְעַשֵּׂר דְּמַאי כְּלוֹקֵחַ מֵעַם הָאָרֶץ:
כסף משנה
8.
[The following rules apply when a person] purchases [produce] from a gentile in the land inhabited by the Jews who ascended from Babylonia. If the gentile was a merchant23If, however, the gentile grew the produce himself, it is exempt from the obligation of tithes. who purchases produce from Jews, the produce is [considered as] demai. Therefore at the outset, when the majority of Eretz Yisrael was in the hands of Jews,24In later eras, by contrast, the land was owned primarily by gentiles and there is no need to consider the produce as demai (Radbaz). when a person purchased produce from a gentile merchant, he would separate tithes as one does for demai just like one does when [purchasing] from a [Jewish] common person.

הלכה ט
אֵי זֶהוּ תַּגָּר זֶה שֶׁהֵבִיא שְׁתַּיִם וְשָׁלֹשׁ פְּעָמִים. אֲבָל אִם הֵבִיא פַּעַם אַחַת אֲפִלּוּ הֵבִיא שָׁלֹשׁ מַשּׂוֹאוֹת בְּבַת אַחַת אוֹ שֶׁהֵבִיא הוּא וּבְנוֹ וּפוֹעֵל עֲדַיִן לֹא הֻחְזַק תַּגָּר:
כסף משנה
9.
Who is a merchant? One who brings [produce to the market] two or three times. If, however, he brings once - even if he brings three loads at once, or even if he, his son, and his servant each brings loads - he is not presumed to be a merchant.25And it is possible that he brought from his own produce.

הלכה י
כְּשֶׁגָּזְרוּ עַל הַדְּמַאי לֹא גָּזְרוּ עַל פֵּרוֹת חוּצָה לָאָרֶץ שֶׁנִּכְנְסוּ לָאָרֶץ:
כסף משנה
10.
When [our Sages] issued a decree concerning demai, the decree did not apply to produce from the Diaspora that was brought into Eretz Yisrael.26The Radbaz states that this applies to produce that was sold to a Jew who completed the tasks associated with its preparation. Even though such produce must be tithed, the stringency of demai does not apply.

הלכה יא
פֵּרוֹת הָאָרֶץ שֶׁרַבּוּ עַל שֶׁל חוּצָה לָאָרֶץ הֲרֵי אֵלּוּ חַיָּבִין בִּדְמַאי. וְשֶׁל חוּצָה לָאָרֶץ שֶׁרַבּוּ עַל פֵּרוֹת הָאָרֶץ. וְכֵן דְּבָרִים שֶׁחֶזְקָתָן תָּדִיר מִחוּצָה לָאָרֶץ כְּגוֹן אֱגוֹזִים וְדֻרְמַסְקָעוֹת הֲרֵי אֵלּוּ פְּטוּרִין מִן הַדְּמַאי:
כסף משנה
11.
When the majority of the produce [in a mixture] is from Eretz Yisrael and not from the Diaspora, [the laws of] demai apply.27For as in all matters, the ruling is dependent on the majority (Radbaz). If the majority of the mixture is produce from the Diaspora, it is exempt from demai. [This law applies] also to species that we can presume that most frequently come from the Diaspora, e.g., nuts and plums.28The particular species of plums the Rambam mentions grew primarily in Damascus and the laws of demai do not apply to produce that grows there (Chapter 12, Halachah 11).

הלכה יב
לֹא הָלְכוּ חֲכָמִים בְּפֵרוֹת חוּצָה לָאָרֶץ לֹא אַחַר הַמַּרְאֶה וְלֹא אַחַר הַטַּעַם וְהָרֵיחַ אֶלָּא אַחַר הָרֹב כָּל שֶׁרַבּוּ לוֹ מֻתָּר וְשֶׁלֹּא רַבּוּ לוֹ אָסוּר. כֵּיצַד. רַבּוּ בָּעִיר אֲבָל לֹא בַּמְּדִינָה. אוֹ שֶׁרַבּוּ בַּמְּדִינָה וְלֹא רַבּוּ בָּעִיר. בָּהָר וְלֹא רַבּוּ בַּבִּקְעָה. בַּבִּקְעָה וְלֹא בָּהָר. רַבּוּ לַחֶנְוָנִי וְלֹא לְבַעַל הַבַּיִת. לְבַעַל הַבַּיִת וְלֹא לַחֶנְוָנִי. זֶה שֶׁרַבּוּ בּוֹ מֻתָּר. וּמָקוֹם שֶׁלֹּא רַבּוּ בּוֹ חַיָּב בִּדְמַאי:
כסף משנה
12.
[When there was a doubt whether] produce came from the Diaspora or not, our Sages [maintained that the ruling] is not dependent on the appearance [of the produce], its flavor, or its fragrance,29I.e., one might say that as a result of these factors one could identify the source of the produce. but rather where the majority [of produce in the marketplace originated]. If produce [from the Diaspora] constitutes the majority, it is permitted.30I.e., without tithing. If not, it is forbidden.
What is implied? When there is a majority [of produce from the Diaspora] in a city, but not in its outlying areas, or in the outlying areas31This is the interpretation of the term medina followed by most authorities. From the Rambam's wording in Hilchot Ishut 13:17, the interpretation of this halachah would be: "When there is a majority in a town, but not in a metropolis...." and not in the city, in the mountain, but not in the valley, in the valley, but not in the mountain, for a storekeeper, but not for a private homeowner, for a private homeowner and not for a storekeeper, for those where [produce from the Diaspora] is the majority, they are permitted.32To partake of it without observing the restrictions of demai. For those where it is not in the majority, they are obligated [to heed the restrictions of] demai.

הלכה יג
רַבּוּ פֵּרוֹת חוּצָה לָאָרֶץ בַּשּׁוּק וְנִתְמַעֲטוּ חָזַר הַשּׁוּק לְיָשְׁנוֹ וְהַלּוֹקֵחַ מִמֶּנּוּ חַיָּב בִּדְמַאי:
כסף משנה
13.
If, at first, there was a majority of produce from the Diaspora in the market place and then, that quantity was reduced, the market place returns to its original status, and one who purchases [produce] is obligated in [the restrictions of] demai.

הלכה יד
וְאֵלּוּ דְּבָרִים שֶׁלֹּא גָּזְרוּ עֲלֵיהֶן בְּשָׁעָה שֶׁגָּזְרוּ עַל הַדְּמַאי. הַלּוֹקֵחַ פֵּרוֹת לִזְרִיעָה אוֹ לְהַאֲכִיל לִבְהֵמָה. קֶמַח לְעוֹרוֹת אוֹ לִמְלוּגְמָא אוֹ לִרְטִיָּה. שֶׁמֶן לְהַדְלָקַת הַנֵּר אוֹ לָסוּךְ בּוֹ אֶת הַכֵּלִים. יַיִן לְקִילוֹר. וְחַלַּת עַם הָאָרֶץ. וְהַמְדֻמָּע. וְהַלָּקוּחַ בְּכֶסֶף מַעֲשֵׂר שֵׁנִי. וּשְׁיָרֵי הַמְּנָחוֹת. וְתוֹסֶפֶת הַבִּכּוּרִים. כָּל אֵלּוּ פְּטוּרִים מִן הַדְּמַאי. וְכֵיוָן שֶׁאָמַר לוֹ עַם הָאָרֶץ מְתֻקָּנִין הֵם אֵינוֹ צָרִיךְ לְעַשֵּׂר:
כסף משנה
14.
At the time the decree concerning demai was issued, it was not applied in the following situations. All of the [following] instances are exempt from the obligations of demai: One who purchases: produce for seed or as animal fodder, flour for the processing of hides33See the Rambam's Commentary to the Mishnah (Demai 1:3) for clarification regarding this and the other subjects mentioned in this halachah. or for a compress or a bandage, oil to kindle a lamp or to apply to utensils, wine for an eye ointment.34Produce used for purposes other than for food. [This ruling also applies to] challah separated by a common person,35For challah like terumah carries a punishment of death at the hand of heaven and even the common people were careful with regard to its observance. a mixture of terumah and ordinary produce,36Since such a mixture contains terumah which involves such a severe penalty, the common people were careful with regard to the prohibitions involved. produce purchased with money from the second tithes,37I.e., after the second tithe is redeemed, the money used for its redemption must be used to purchase food in Jerusalem. flour left over from a meal offering,38The priest would take a handful of flour from a meal offering to offer on the altar. The remainder was eaten by the priests. We do not suspect that the remainder was demai. and produce added to the bikkurim offerings.39The first fruits of the seven species for which Eretz Yisrael is praised must be brought to the Temple and given to the priests as the bikkurim offerings. Occasionally, fruits of the same species were added to the offering to make it more impressive. These are referred to as "produce added to the bikkurim." If a common person tells him that the appropriate separations have been made, there is no obligation to tithe it.40Nevertheless, even in these instances, the initial preference should be to purchase the produce from a trustworthy source (Radbaz).

הלכה טו
הַלּוֹקֵחַ פֵּרוֹת לַאֲכִילָה וְנִמְלַךְ עֲלֵיהֶם לִבְהֵמָה הֲרֵי זֶה לֹא יִמְכְּרֵם לְעַכּוּ''ם. וְלֹא יַאֲכִילֵם לִבְהֵמָה אֲפִלּוּ לְבֶהֱמַת אֲחֵרִים עַד שֶׁיְּתַקְּנֵם דְּמַאי:
כסף משנה
15.
When a person purchases produce to eat and changed his mind and thought to use it as animal fodder, he should not sell them to a gentile41The separations are necessary in this instance, for the gentile may sell the produce to another Jew (Radbaz). or feed them to an animal - even an animal belonging to others - until he makes the separations associated with demai.42For once he has incurred the obligation to make the separations associated with demai, he is not absolved from that responsibility until he does so (ibid.).

הלכה טז
שֶׁמֶן עָרֵב פָּטוּר מִן הַדְּמַאי שֶׁאֵין חֶזְקָתוֹ לַאֲכִילָה. שֶׁמֶן שֶׁלָּקַח הַסּוֹרֵק לְתִתּוֹ בְּצֶמֶר פָּטוּר מִן הַדְּמַאי מִפְּנֵי שֶׁהוּא נִבְלָע בַּצֶּמֶר. אֲבָל שֶׁמֶן שֶׁלּוֹקֵחַ הָאוֹרֵג לָסוּךְ בֵּין אֶצְבְּעוֹתָיו חַיָּב בִּדְמַאי מִפְּנֵי שֶׁהוּא נִבְלָע בְּגוּפוֹ וְסִיכָה הִיא כִּשְׁתִיָּה בְּכָל מָקוֹם:
כסף משנה
16.
Fragrant oil43Olive oil mixed with fragrant spices [Rav Kappach's translation of the Rambam's Commentary to the Mishnah (Demai 1:3)]. is exempt from [the obligations of] demai for we assume it will not be eaten. When a comber of wool purchases oil to put it in the wool,44Wool would be combed to remove its dirt and other impurities attached to it. Oil was applied to the wool to make the combing process easier. it is exempt from [the obligations of] demai, because it is absorbed by the wool.45Like the oil applied to utensils mentioned in Halachah 14. When, however, a weaver purchases oil to apply between his fingers,46As protection for them in the weaving process. it is obligated in [the laws of] demai. The rationale is that it is absorbed in his body and the application of oil is considered as drinking in all instances.47See Hilchot Shivitat Esor 1:5.

הלכה יז
עַכּוּ''ם שֶׁשָּׁאַל מִיִּשְׂרָאֵל לִתֵּן לוֹ שֶׁמֶן עַל מַכָּתוֹ אָסוּר בְּוַדַּאי וּמֻתָּר בִּדְמַאי. נָתַן הָעַכּוּ''ם שֶׁמֶן עַל גַּבֵּי טַבְלָא לְהִתְעַגֵּל עָלֶיהָ מִשֶּׁעָמַד מֻתָּר לְיִשְׂרָאֵל לֵישֵׁב אַחֲרָיו:
כסף משנה
17.
When a gentile asks a Jew to place oil on his wound,48I.e., he is asking a chavair to use the chavair's own oil for this purpose. he is forbidden to use oil from which he is certain the appropriate separations have not been made. He is, however, permitted to use demai for this purpose.49As a salve. If a chavair knows that produce has not been tithed, he may not use it in a manner that removes it from his possession or destroys it until he tithes it. For using it to benefit another person is equivalent to a sale (Chasdai David). With regard to demai, however, leniency may be shown, for he is using it for medical purposes for a gentile. If, however, he is using it for a Jew, the tithes must be separated even in this instance. If a gentile places oil50This refers even to oil from which we are certain separations have not been made. on a tablet to twist around,51One of the ways people would apply oil to their flesh was to place it on a marble tablet and then roll on the tablet. after he arises, it is permitted for a Jew to sit on it afterwards.52Even though the oil will be applied to his flesh. The rationale is that once the gentile used it, the holiness vested in the terumah has been defiled and it is no longer necessary to make any separations from it. Note a parallel in Hilchot Terumot 11:8 (Chasdei David). In this instance, we are speaking about demai (which is feared to be tevel) and not terumah and in its present state, it is not holy. Nevertheless, the same principles can be applied.

הלכה יח
מִי שֶׁנָּפַל שֶׁמֶן דְּמַאי עַל בְּשָׂרוֹ מְשַׁפְשְׁפוֹ וְאֵינוֹ חוֹשֵׁשׁ. הַלּוֹקֵחַ יַיִן לְמֻרְיָס אוֹ לַאֲלוּנְתִּית. אוֹ קִטְנִיּוֹת לַעֲשׂוֹת טְחִינִין חַיָּב בִּדְמַאי. אֲבָל הַלּוֹקֵחַ מֻרְיָס שֶׁיֵּשׁ בּוֹ יַיִן אוֹ אֲלוּנְתִּית אוֹ שֶׁלָּקַח טְחִינִין הֲרֵי אֵלּוּ פְּטוּרִין מִן הַדְּמַאי שֶׁלֹּא גָּזְרוּ עַל תַּעֲרֹבֶת דְּמַאי. וְאִם הָיָה הַדָּבָר שֶׁחַיָּב בִּדְמַאי שֶׁנִּתְעָרֵב כְּגוֹן תַּבְלִין וּשְׂאוֹר הוֹאִיל וְטַעֲמוֹ נִכָּר אֵינָן בְּטֵלִים וְנִמְצֵאת כָּל הַתַּעֲרוֹבֶת חַיֶּבֶת בִּדְמַאי:
כסף משנה
18.
When oil that is demai falls on a person's flesh, he may rub it without concern.53As mentioned above, one should not apply oil that is demai to one's body. In this instance, however, the oil fell on the person's body against his will and its holiness is defiled at that time. Hence, what happens afterwards is not significant and he can continue rubbing that oil into to his flesh. When a person purchases wine for fishbrine or a mixture of wine and water or legumes to crush and mix with honey, he is obligated in the restrictions of demai.54Because they were already distinct entities obligated in the restrictions of demai before the mixture came into being. If, however, he purchased fishbrine that contains wine, a mixture of wine and oil, or a mixture of crushed legumes and honey, he is exempt from the restrictions of demai, for [our Sages] did not apply their decree to a mixture of demai and other substances. If the entity that was demai that became mixed with other substances was something like spices or yeast,55I.e., an entity that has an effect that is far greater than what could be expected from its size. This is a general principle applied with regard to all of the Torahs prohibitions; see Hilchot Ma'achalot Assurot 16:1-2. since its flavor is evident, the restrictions involving demai must be observed for the entire mixture.

הלכה יט
כָּל אֵלּוּ הַפְּטוּרִין מִן הַדְּמַאי שֶׁלֹּא גָּזְרוּ עֲלֵיהֶם. אִם הִתְקִינָן דְּמַאי וְהִפְרִישׁ מֵהֶם תְּרוּמַת מַעֲשֵׂר וּמַעֲשֵׂר שֵׁנִי מַה שֶּׁעָשָׂה עָשׂוּי. אֲבָל אִם תִּקֵּן אֶת הַדְּמַאי בְּוַדַּאי וְהִפְרִישׁ מִמֶּנּוּ תְּרוּמָה גְּדוֹלָה וּמַעַשְׂרוֹת אוֹ שֶׁתִּקֵּן אֶת הַוַּדַּאי בִּדְמַאי לֹא עָשָׂה כְּלוּם:
כסף משנה
19.
In all those situations where one is exempt from demai because [our Sages] did not apply their decree in these instances, if one corrected [the produce as one does] demai, separating terumat ma'aser and the second tithe, his actions are considered of consequence.56He must give the terumat ma'aser to a priest and redeem the second tithe and use it to purchase food in Jerusalem. If, however, he sought to correct [produce that is] demai like one does produce from which we are certain that no separations were made,57Our translation follows the text suggested by the Kessef Mishneh. It is found in several authentic manuscripts of the Mishneh Torah. The version in the standard printed text - which was also the version possessed by the Ra'avad - differs slightly. separating the great terumah and the tithes from it58This is unnecessary, for we assume that terumah has already been separated. With regard to the tithes - the first tithe and the tithe for the poor - for demai, it is not necessary to give these to the Levite and the poor person, as one does when he is certain that the separations have not been made. Instead, all that is necessary is to make the separations. or he sought to correct produce from which we are certain that no separations were made by making separations like one does demai, his deeds are of no consequence.59In the latter instance, his deeds are of no consequence, because since he is not separating the great terumah, he is making the separations in improper order. Since that is undesirable, we assume that had he known what he was required to do, he would have made the separations in the appropriate order. Hence the separation that he did make is considered to have been made in error and therefore invalid.

הלכה כ
כָּל הָעִיר מוֹכְרִין וַדַּאי וְאֶחָד מוֹכֵר דְּמַאי וְלָקַח וְאֵין יָדוּעַ מִמִּי לָקַח כֵּיצַד מְתַקֵּן. מַפְרִישׁ תְּרוּמָה וּתְרוּמַת מַעֲשֵׂר וְנוֹתְנָן לְכֹהֵן וּמַפְרִישׁ מַעֲשֵׂר שֵׁנִי בִּלְבַד וַהֲרֵי הוּא כְּמַעֲשֵׂר שֵׁנִי שֶׁל דְּמַאי:
כסף משנה
20.
[The following laws apply when] all [of the individuals in] a town sell produce that is definitely [tevel], one person sells demai , and one purchases [produce] from a person without knowing from whom he purchased. How should he correct the produce?60Because it is possible that it is demai and it is possible that it is definitely tevel. Generally, we follow the principle that whenever the existence of an entity is fixed, we do not look at the actual ratio of permitted and forbidden entities. Instead, we consider it as if half are forbidden and half are permitted (see Hilchot Ma'achalot Assurot 8:11) . Now, in this instance, there is a stringency in considering the produce as tevel - that one must separate the great terumah. And there is a stringency in considering the produce as demai - that he must separate terumat ma'aser and the second tithe. To permit the use of the produce, he must fulfill both stringencies. He must also separate the first tithe and the tithe for the poor. He does not have to give this produce away, because of the doubt concerning its status. Instead, he may keep it for himself. He should separate terumah and terumat ma'aser and give it to the priest. And then he should separate the second tithe and it is considered as the second tithe of demai.

הלכה כא
וְכֵן אִם הָיוּ לְפָנָיו שְׁתֵּי קֻפּוֹת אַחַת טֶבֶל וְאַחַת מְתֻקָּן וְאָבְדָה אַחַת מֵהֶם הֲרֵי זֶה מַפְרִישׁ מִן הַשְּׁנִיָּה תְּרוּמָה גְּדוֹלָה וּתְרוּמַת מַעֲשֵׂר וְנוֹתְנָן לְכָל כֹּהֵן שֶׁיִּרְצֶה וּמַפְרִישׁ מַעֲשֵׂר שֵׁנִי בִּלְבַד בִּדְמַאי:
כסף משנה
21.
Similar [concepts apply] if there were two containers [of produce] before a person: one containing tevel and one containing produce from which the separations were made. If one of them is lost,61But we do not know which one. one must separate terumah and terumat ma'aser from the other one and give it to any priest he desires. And he should separate the second tithe and it is considered as the second tithe of demai.62In this instance as well, since it is possible that the separations have already been made, we do not require him to give the first tithe and the tithe of the poor. Those separations that involve prohibitions, by contrast, must be made.

זרעים הלכות מעשרות פרק יג
Zeraim Maaser Chapter 13