| John Bell - 1790
...having discovered the demonstration of the 47th proposition of the first book of Euclid, viz. that in n **right angled triangle the square of the hypothenuse is equal to the sum of the** squares of the two other sides. Julius Capito/ linus relates, that when an Hecatomb was to be sacrificed,... | |
| Abel Flint - 1804 - 168 Seiten
...be found by the Square Root, without finding the Angles ; according to the following PROPOSITION : **In every Right Angled Triangle, the Square of the Hypothenuse is equal to the Sum of the** Squares of the two Legs. Hence, The Square of the given Leg being subtracted from the Square of the... | |
| Abel Flint - 1808 - 168 Seiten
...be found by the Square Root, without Finding the Angles ; according to the following PROPOSITION : **In every Right Angled Triangle, the Square of the Hypothenuse is equal to the Sum of the** Squares of the two Legs. Hence, The Square of the given Leg being subtracted from the Square of the... | |
| Jeremiah Day - 1815 - 96 Seiten
...referred to. 94. Other relations of the sine, tangent, Sic. may be derived from the proposition, that **the square of the hypothenuse is equal to the sum of the** squares of the perpendicular sides. (Euc. 47. I.) In the right angled triangles CBG, CAD, and CHF,... | |
| Jeremiah Day - 1815 - 126 Seiten
...the third side may be found, without the aid of the trigonometrical tables, by the proposition, that **the square of the hypothenuse is equal to the sum of the** squares of the two perpendicular sides. (Euc. 47. 1.) If the legs be given, extracting the square root... | |
| Thomas Keith, William Hawney - 1817
...arc AD B. 4. An angle IAD in a semi'circle is a right angle (EUCLID 31 ./III.) 5. In a right-angled **triangle the square of the hypothenuse is equal to the sum of the** squares of the other two sides, (EuctiD 47 «/"!.) see also Problem VI. 6. If a perpendicular be drawn... | |
| 1818
...observes: •;•• ,'.I asked the Japanese academician whether he was perfectly convinced that in a **right angled triangle the square of the hypothenuse is equal to the** squares of the other two sides ? He answered in the affirmative. I then asked how they were certain... | |
| William Nicholson - 1819
...which subtends the right angle. Euclid, lib. i. proposition 47, demonstrates, that in every rectilmear **right angled triangle, the square of the hypothenuse is equal to the** squares of both the other sides. This celebrated problem was discovered by Pythagoras, who is said... | |
| Adrien Marie Legendre - 1819 - 208 Seiten
...others ; for the three figures will be proportional to the squares of their homologous sides ; now **the square of the hypothenuse is equal to the sum of the** squares of the two other sides ; therefore, &c. THEOREM. 223. The parts of two chards which cut each... | |
| William Nicholson - 1821
...right-angled triangles, which are similar to the first triangle, and to one another. In every right-angled **triangle, the square of the hypothenuse is equal to the sum of the** squares of the other two sides; and, in general, any figure described on the hypothenuse is equal to... | |
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