The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 51
... described on BC , and the squares GB , HC on BA , AC . Therefore the square described on the side BC is equal to the squares described on the sides BA , AC . Wherefore , in any right - angled triangle & c . Q.E.D. PROPOSITION 48 ...
... described on BC , and the squares GB , HC on BA , AC . Therefore the square described on the side BC is equal to the squares described on the sides BA , AC . Wherefore , in any right - angled triangle & c . Q.E.D. PROPOSITION 48 ...
Página 211
... described on BC shall be equal to the similar and similarly described figures on BA and CA. Draw the perpendicular [ I. 12 . AD . Then , because in the right- angled triangle ABC , AD is drawn from the right angle at A , perpendicular ...
... described on BC shall be equal to the similar and similarly described figures on BA and CA. Draw the perpendicular [ I. 12 . AD . Then , because in the right- angled triangle ABC , AD is drawn from the right angle at A , perpendicular ...
Página 270
... described on the first side would then be less than the sum of the squares described on the other two sides , by II . 13 ; therefore the angle must be obtuse . Similarly we may demonstrate the following , which is the con- verse of II ...
... described on the first side would then be less than the sum of the squares described on the other two sides , by II . 13 ; therefore the angle must be obtuse . Similarly we may demonstrate the following , which is the con- verse of II ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore