 | Euclid - Geometry - 1845 - 218 pages
...AC, and twice the rectangle CB, BD ; that is, the square of AC alone is less than the squares of CB, BA, by twice the rectangle CB, BD. Secondly, let AD...right angle, the angle ACB is greater § than a right J ' 18.1> angle ; and therefore the square of AB is // equalIT to the squares of AC, CB, and // * 12.... | |
 | Euclides - 1845 - 546 pages
...AC, and twice the rectangle CB, BD ; that is, the square of AC alone is less than the squares of CB, BA, by twice the rectangle CB, BD. Secondly, let .AD fall without the triangle ABC. A Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i.... | |
 | Euclides - 1846 - 292 pages
...is, the square of AC alone is less than the squares of CB, BA, by twice the rectangle CB, BD. Next, let AD fall without the triangle ABC : Then, because...angle, the angle ACB is greater than a right angle (1. 16) ; and therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...DA2=AC2 (47. 1.) ; therefore BC2+AB2= 2BC.BD + AC2 ; that is, AC2 is less than BC2+AB2by2BC.BD. B nc Secondly, let AD fall without the triangle ABC :*...angle at D is a right angle, the angle ACB is greater (16. 1.) than a right angle, and AB2= (12. 2.) AC2+BC2+2BC.CD. Add BC2 to each; then AB2 + BC2=A.C2-f2BC2+2BC.CD.... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...AC, and twice the rectangle CB, BD, that is, the square of AC alone is less than the squares of CB, BA by twice the rectangle CB, BD. Secondly, let AD fall without the triangle A ABC : Then, because the angle at D is a right angle, the angle ACB is greater (i. 16.) than a right... | |
 | Euclides - 1852 - 152 pages
...square of AC alone is less than the squares of CB, BA by twice the rectangle CB, BD. BOOK^II. CASE II. Secondly, let AD fall without the triangle ABC: Then, because the angle at D is a right angle, 4 xvi. i. the angle ACB is greater 11 than a right angle; and therefore the square of AB is xii. 2.... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...AC, and twice the rectangle CB, BD ; that is, the square of AC alone is less than the squares of CB, BA, by twice the rectangle CB, BD. Secondly, let AD...angle at D is a right angle, the angle ACB is greater (16. i.) than a right angle ; and therefore the square of AB is equal (12. n.) to the squares of AC,... | |
 | Euclides - 1853 - 146 pages
...AC, and twice the rectangle CB,BD; that is, the square of AC alone is less than the squares of CB, BA, by twice the rectangle CB, BD. Secondly, let AD fall without the triangle ABC. A fl B CD Then, because the angle at D is a right angle, (I. 16.) 1. The angle ACB is greater than... | |
 | Euclides - Geometry - 1853 - 176 pages
...squares of С b, ba by twice the rectangle С b, b d. Secondly, let ad fall without the triangle abС. Then, because the angle at d is a right angle, the angle a С b is greater (i. 1 6) than a right angle ; and therefore the square of ab is equal (ii. 12) to... | |
 | Euclides - 1856 - 168 pages
...rectangle BC, B T>. Secondly, let AD fall without the triangle ABC (Fig. 42). Then, because the angle ADB is a right angle, the angle ACB is greater than a right angle, and therefore the square of AB (Prop. 55), is equal to the squares of AC, BC and twice the rectangle... | |
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CB, BA, by twice the rectangle CB, BD. Secondly, Let AD fall without the triangle ABC. Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i. 
