...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,...

...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...

...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...

...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,...

...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...

...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...

...consequents FGH+FHI+F1K, or the polygon FGHIK, as one antecedent ABC is to its consequent FGH, or as . .'// is to FG (219). Therefore the surfaces of similar...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...

...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...

...three angles of a triangle are equal to two right angles ; and also, that in any right-angled triangle the square of the hypothenuse is equal to the sum of the squares of the other two sides. In like manner did this ingenious gentleman demonstrate, that it was...

...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...