PARSHA MATH
KETORES
שמות פרק ל לד וַיֹּאמֶר ה' אֶל-משֶה קַח -לְךָ סַמִּים נָטָף וּשְחֵלֶת וְחֶלְבְנָה סַמִּים וּלְבֹּנָה זַכָה בַד בְבַד יִּהְיֶה:
And the L-rd said unto Moses: Take unto thee sweet spices, balsam, and onycha and galbanam, sweet spices, with pure frankincense.
The Rabbis learn that Ketores has eleven principal ingredients (כריתות ו' ב'). How do they learn the concept of eleven from this verse?
Complete the following chart by entering the appropriate number and learn how the verse indicates eleven
- סמים General term for spices (minimum of two)
- נטף Name of one spice plus
- שחלת Name of one spice plus
- חלבנה Name of one spice plus
- סמים General term for spices (can not be two since already used; thus, must be equal to all the prior values presented so far in this verse) plus
- לבנה Name of one spice plus
שמות פרק ל לז : וְהַקְטֹּרֶת אֲשֶר תַעֲשֶה בְמַתְכֻּנְתָהּ לֹּא תַעֲשוּ לָכֶם קֹּדֶש תִּהְיֶה לְךָ לַה ' :
Count the number of words in the above verse:
LUCHOS
Moshe brought down two identical Luchos. Each Luach (Tablet) was 6 tefachim high and six tefachim wide and its depth was three tefachim. (A tefach is approximately 3-4 inches; each Luach was 18-24 inches by 18-24 inches by 9-12 inches)
Four opinions as to how many Commandments were written on each Luach:
5 Commandments 20 Commandments
10 Commandments 40 Commandments
Rema from Pano says the each opinion is correct. Each one is describing a different view.
How can each opinion be correct?
How many sides to a cube shape?
How many types of surface areas on each Luach?
Hint (10 +10 + 5 + 5 + 5 + 5)
Each Luach is a rectangular cube (three dimensions are not equal). Can the Luchos be placed together to form a perfect cub (all three dimensions are equal)?
How can each opinion be correct?
On the front and back sides of each Luach, there was a surface of six by six tefachim on which to write all Ten Commandments. However, on the sides, top and bottom of the Luchos, the surface was only three by six tefachim. Only five Commandments were written on the sides, top and bottom. It comes out that each Luach had Ten Commandments on front, ten on back, five on the top, bottom, right and left sides, for a total of forty commandments on each Luach.
When Moshe Rabbeinu descended from Har Sinai, he held the Luchos one in front of the other. The writing was visible only from the sides, where five Commandments were seen on each Luach.
ONE: one side area seen
Surface area of three by six
Appearing to hold five Commandments each Luach
Later, Moshe separated them and revealed that on the front of each Luach were all Ten Commandments.
TWO: one front area seen
Surface area of six by six
Appearing to hold 10 commandments each Luach
Afterwards Moshe held them up for Bnei Yisroel to see, the Ten Commandments could be seen on both the front and back; a total of 20 on each Luach.
THREE: one front area and one back area seen
Surface area of six by six for each
Appearing to hold 20 commandments each Luach
Finally. Moshe placed the Luchos before Bnei Yisrael to investigate more thoroughly, they saw that five Commandments were written on each side, plus the front and the back had 10 more each or a total of forty commandments on each Luach.
FOUR: one front area, one back area and four side areas were seen
Appearing to hold 40 commandments each (10 +10 +5 +5 +5 +5)
Four side areas front and back
How many sides to a cube shape? Six
How many types of surface areas on each Luach? Two (6 X 6 and 3 X 3)
Hint (10 +10 + 5 + 5 + 5 + 5)
Each Luach is a rectangular cube (three dimensions are not equal). Can the Luchos be placed together to form a perfect cub (all three dimensions are equal)?
If placed in one in front of the other, then the depth becomes 6 tefachim and the two “jointed” Luchos would become perfect cubes (per Rema from Pano, this was the initial presentation from Moshe to Bnei Yisrael).
