New Plane Geometry
New Plane Geometry
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In our eReader you can find the full English version of the book. Read New Plane Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book New Plane Geometry
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Theorem 218. (Converse of Prop. I.) If the product of two numbers is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion.
Given ad=:bc. (1) To Prove - = ^.
b d Proof. Dividing both members of (1) by bd, (id__bc 2i — l bd^bd'^^ b'^d' In like manner, we may prove - = - ; - = - ; etc.
c d a c Prop. III. Theorem 219. In any proportion, the terms are in proportion by Alter- nation; that is, the first term is to the third as the second ...term is to the fourth.
Given the proportion - = -. (1) a PROPORTION 103 To Prove 5 = ^.
c d Proof. From (1), ad = be. (§ 216) Then, 2 = 1 (§218) Prop. IV. Theorem 220. In any proportion, the terms are in proportion by Inver- sion ; that iSy the second term is to the first as the fourth term is to the third.
Given the proportion - = -. (1) a To Prove ^ = ^.
a c Proof. From (1), ad = be. (?) Then, ^ = ^. (?) a c Prop. V. Theorem 221. In any proportion, the terms are in proportion by Com- position ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
What to read after New Plane Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Webster Wells to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Theorem 218. (Converse of Prop. I.) If the product of two numbers is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion.
Given ad=:bc. (1) To Prove - = ^.
b d Proof. Dividing both members of (1) by bd, (id__bc 2i — l bd^bd'^^ b'^d' In like manner, we may prove - = - ; - = - ; etc.
c d a c Prop. III. Theorem 219. In any proportion, the terms are in proportion by Alter- nation; that is, the first term is to the third as the second ...term is to the fourth.
Given the proportion - = -. (1) a PROPORTION 103 To Prove 5 = ^.
c d Proof. From (1), ad = be. (§ 216) Then, 2 = 1 (§218) Prop. IV. Theorem 220. In any proportion, the terms are in proportion by Inver- sion ; that iSy the second term is to the first as the fourth term is to the third.
Given the proportion - = -. (1) a To Prove ^ = ^.
a c Proof. From (1), ad = be. (?) Then, ^ = ^. (?) a c Prop. V. Theorem 221. In any proportion, the terms are in proportion by Com- position ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
What to read after New Plane Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Webster Wells to read onlineMoreLess
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