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Talmud Tuesdays - Rosh Chodesh
(ב) הַחֹ֧דֶשׁ הַזֶּ֛ה לָכֶ֖ם רֹ֣אשׁ חֳדָשִׁ֑ים רִאשׁ֥וֹן הוּא֙ לָכֶ֔ם לְחָדְשֵׁ֖י הַשָּׁנָֽה׃
(2) This month shall mark for you the beginning of the months; it shall be the first of the months of the year for you.
בראשית. אָמַר רַבִּי יִצְחָק לֹֹֹֹֹא הָיָה צָרִיךְ לְהַתְחִיל אֶת הַתּוֹרָה אֶלָּא מֵהַחֹדֶשׁ הַזֶּה לָכֶם, שֶׁהִיא מִצְוָה רִאשׁוֹנָה שֶׁנִּצְטַוּוּ בָּהּ יִשׂרָאֵל, וּמַה טַּעַם פָּתַח בִּבְרֵאשִׁית? מִשׁוּם כֹּחַ מַעֲשָׂיו הִגִּיד לְעַמּוֹ לָתֵת לָהֶם נַחֲלַת גּוֹיִם (תהילים קי"א), שֶׁאִם יֹאמְרוּ אֻמּוֹת הָעוֹלָם לְיִשְׁרָאֵל לִסְטִים אַתֶּם, שֶׁכְּבַשְׁתֶּם אַרְצוֹת שִׁבְעָה גוֹיִם, הֵם אוֹמְרִים לָהֶם כָּל הָאָרֶץ שֶׁל הַקָּבָּ"ה הִיא, הוּא בְרָאָהּ וּנְתָנָהּ לַאֲשֶׁר יָשַׁר בְּעֵינָיו, בִּרְצוֹנוֹ נְתָנָהּ לָהֶם, וּבִרְצוֹנוֹ נְטָלָהּ מֵהֶם וּנְתָנָהּ לָנוּ:

בראשית IN THE BEGINNING — Rabbi Isaac said: The Torah which is the Law book of Israel should have commenced with the verse (Exodus 12:2) “This month shall be unto you the first of the months” which is the first commandment given to Israel. What is the reason, then, that it commences with the account of the Creation? Because of the thought expressed in the text (Psalms 111:6) “He declared to His people the strength of His works (i.e. He gave an account of the work of Creation), in order that He might give them the heritage of the nations.” For should the peoples of the world say to Israel, “You are robbers, because you took by force the lands of the seven nations of Canaan”, Israel may reply to them, “All the earth belongs to the Holy One, blessed be He; He created it and gave it to whom He pleased. When He willed He gave it to them, and when He willed He took it from them and gave it to us” (Yalkut Shimoni on Torah 187).

(טז) וַיַּ֣עַשׂ אֱלֹהִ֔ים אֶת־שְׁנֵ֥י הַמְּאֹרֹ֖ת הַגְּדֹלִ֑ים אֶת־הַמָּא֤וֹר הַגָּדֹל֙ לְמֶמְשֶׁ֣לֶת הַיּ֔וֹם וְאֶת־הַמָּא֤וֹר הַקָּטֹן֙ לְמֶמְשֶׁ֣לֶת הַלַּ֔יְלָה וְאֵ֖ת הַכּוֹכָבִֽים׃
(16) God made the two great lights, the greater light to dominate the day and the lesser light to dominate the night, and the stars.
רבי שמעון בן פזי רמי כתיב (בראשית א, טז) ויעש אלהים את שני המאורות הגדולים וכתיב את המאור הגדול ואת המאור הקטן אמרה ירח לפני הקב"ה רבש"ע אפשר לשני מלכים שישתמשו בכתר אחד אמר לה לכי ומעטי את עצמך אמרה לפניו רבש"ע הואיל ואמרתי לפניך דבר הגון אמעיט את עצמי אמר לה לכי ומשול ביום ובלילה אמרה ליה מאי רבותיה דשרגא בטיהרא מאי אהני אמר לה זיל לימנו בך ישראל ימים ושנים אמרה ליה יומא נמי אי אפשר דלא מנו ביה תקופותא דכתיב (בראשית א, יד) והיו לאותות ולמועדים ולימים ושנים זיל ליקרו צדיקי בשמיך (עמוס ז, ב) יעקב הקטן שמואל הקטן (שמואל א יז, יד) דוד הקטן חזייה דלא קא מיתבא דעתה אמר הקב"ה הביאו כפרה עלי שמיעטתי את הירח והיינו דאמר ר"ש בן לקיש מה נשתנה שעיר של ראש חדש שנאמר בו (במדבר כח, טו) לה' אמר הקב"ה שעיר זה יהא כפרה על שמיעטתי את הירח
§ Rabbi Shimon ben Pazi raises a contradiction between two verses. It is written: “And God made the two great lights” (Genesis 1:16), and it is also written in the same verse: “The greater light to rule the day, and the lesser light to rule the night,” indicating that only one was great. Rabbi Shimon ben Pazi explains: When God first created the sun and the moon, they were equally bright. Then, the moon said before the Holy One, Blessed be He: Master of the Universe, is it possible for two kings to serve with one crown? One of us must be subservient to the other. God therefore said to her, i.e., the moon: If so, go and diminish yourself. She said before Him: Master of the Universe, since I said a correct observation before You, must I diminish myself? God said to her: As compensation, go and rule both during the day along with the sun and during the night. She said to Him: What is the greatness of shining alongside the sun? What use is a candle in the middle of the day? God said to her: Go; let the Jewish people count the days and years with you, and this will be your greatness. She said to Him: But the Jewish people will count with the sun as well, as it is impossible that they will not count seasons with it, as it is written: “And let them be for signs, and for seasons, and for days and years” (Genesis 1:14). God said to her: Go; let righteous men be named after you. Just as you are called the lesser [hakatan] light, there will be Ya’akov HaKatan, i.e., Jacob our forefather (see Amos 7:2), Shmuel HaKatan the tanna, and David HaKatan, i.e., King David (see I Samuel 17:14). God saw that the moon was not comforted. The Holy One, Blessed be He, said: Bring atonement for me, since I diminished the moon. The Gemara notes: And this is what Rabbi Shimon ben Lakish says: What is different about the goat offering of the New Moon, that it is stated with regard to it: “For the Lord” (Numbers 28:15)? The Holy One, Blessed be He, said: This goat shall be an atonement for Me for having diminished the size of the moon.
שעירי ראשי חדשים איצטריכא ליה סלקא דעתך אמינא הא לא כתיב בהו מועד קא משמע לן דראש חדש איקרי מועד

It was necessary for the mishna to mention the goats sacrificed on the New Moons. It could enter your mind to say that since the term appointed time is not written with regard to them, these offerings do not override Shabbat or ritual impurity as do other communal offerings during their appointed times. Therefore, it teaches us that even the New Moon is called a mo'ed, a holiday.

איני והתני רבה בר שמואל יכול כשם שמעברין את השנה לצורך כך מעברין את החדש לצורך ת"ל (שמות יב, ב) החדש הזה לכם ראש חדשים כזה ראה וקדש
§ It was taught above that for various reasons a month can have an extra day added, even if the new moon was seen on the night before the thirtieth. The Gemara challenges this assumption: Is that so? But didn’t Rabba bar Shmuel teach in a baraita: One might have thought that just as the court adds an extra month to a year for some pressing communal need, so too, the court adds an extra day to a month for some similar need. Therefore, the verse states: “This month shall be to you the beginning of months” (Exodus 12:2). This teaches that when there is a moon like this, see it and sanctify the month. When the new moon is seen, the month must be sanctified without delay.
אמר ליה רב אחא מדיפתי לרבינא וליבריך הטוב והמטיב אמר ליה אטו כי חסר מי מברכינן דיין האמת דלבריך הטוב והמטיב וליברכינהו לתרוייהו כיון דהיינו אורחיה לא מברכינן וא"ר אחא בר חנינא א"ר אסי א"ר יוחנן כל המברך על החדש בזמנו כאילו מקבל פני שכינה כתיב הכא (שמות יב, ב) החדש הזה וכתיב התם (שמות טו, ב) זה אלי ואנוהו תנא דבי רבי ישמעאל אילמלא (לא) זכו ישראל אלא להקביל פני אביהן שבשמים כל חדש וחדש דיים אמר אביי הלכך נימרינהו מעומד
§ Rav Aḥa of Difti said to Ravina: And they should bless the blessing of: Blessed are You, Lord our God, King of the Universe, Who is good and Who does good, for the benefit that people derive from the light of moon. Ravina said to him: Is that to say that when the moon is shrinking we bless, as we do for other disasters: Blessed are You, Lord our God, King of the Universe, the true Judge, so that we should conversely bless: Blessed are You, Lord our God, King of the Universe, Who is good and Who does good, when the moon is growing? Rav Aḥa of Difti said to him: You are correct, and we should say them both: The blessing of the true Judge, when the moon is waning, and the blessing of Who is good and Who does good, when the moon is waxing. Ravina answered him: Since this is its nature, we do not bless the moon. The waxing and waning of the moon is not an unexpected occurrence that requires these blessings. And Rabbi Aḥa bar Ḥanina says that Rabbi Asi says that Rabbi Yoḥanan says: With regard to anyone who blesses the new month in its proper time, it is as if he greets the Face of the Divine Presence. Alluding to this, it is written here concerning the sanctification of the new month: “This month shall be for you the beginning of months” (Exodus 12:2), and it is written there, where the Jewish people encountered the Divine Presence at the splitting of the sea: “This is my God and I will glorify Him” (Exodus 15:2). The term “this” is employed in both verses. The school of Rabbi Yishmael taught: If the Jewish people merited to greet the Face of their Father in Heaven only one time each and every month, it would suffice for them, since in the blessing of the moon there is an aspect of greeting the Divine Presence. Abaye said: Therefore, we will say the blessing while standing, in honor of the Divine Presence.
(א) וַיַּ֣רְא הָעָ֔ם כִּֽי־בֹשֵׁ֥שׁ מֹשֶׁ֖ה לָרֶ֣דֶת מִן־הָהָ֑ר וַיִּקָּהֵ֨ל הָעָ֜ם עַֽל־אַהֲרֹ֗ן וַיֹּאמְר֤וּ אֵלָיו֙ ק֣וּם ׀ עֲשֵׂה־לָ֣נוּ אֱלֹהִ֗ים אֲשֶׁ֤ר יֵֽלְכוּ֙ לְפָנֵ֔ינוּ כִּי־זֶ֣ה ׀ מֹשֶׁ֣ה הָאִ֗ישׁ אֲשֶׁ֤ר הֶֽעֱלָ֙נוּ֙ מֵאֶ֣רֶץ מִצְרַ֔יִם לֹ֥א יָדַ֖עְנוּ מֶה־הָ֥יָה לֽוֹ׃ (ב) וַיֹּ֤אמֶר אֲלֵהֶם֙ אַהֲרֹ֔ן פָּֽרְקוּ֙ נִזְמֵ֣י הַזָּהָ֔ב אֲשֶׁר֙ בְּאָזְנֵ֣י נְשֵׁיכֶ֔ם בְּנֵיכֶ֖ם וּבְנֹתֵיכֶ֑ם וְהָבִ֖יאוּ אֵלָֽי׃ (ג) וַיִּתְפָּֽרְקוּ֙ כָּל־הָעָ֔ם אֶת־נִזְמֵ֥י הַזָּהָ֖ב אֲשֶׁ֣ר בְּאָזְנֵיהֶ֑ם וַיָּבִ֖יאוּ אֶֽל־אַהֲרֹֽן׃
(1) When the people saw that Moses was so long in coming down from the mountain, the people gathered against Aaron and said to him, “Come, make us a god who shall go before us, for that man Moses, who brought us from the land of Egypt—we do not know what has happened to him.” (2) Aaron said to them, “Take off the gold rings that are on the ears of your wives, your sons, and your daughters, and bring them to me.” (3) And all the people took off the gold rings that were in their ears and brought them to Aaron.
Pirkei d' R. Elizer
When the men came to take their wives' gold earrings for the golden calf, the women refused to hand them over. They told their husbands, "We will not obey you and help you make an abomination that has no power or salvation." God rewarded them in this world [for this refusal] by granting them a greater degree of observance on Rosh Chodesh. And God rewards them in the World to Come by giving them the power of constant renewal which characterizes Rosh Chodesh.
(Book of our Heritage, Eliyahu Ki Tov, pg. 222)