Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 19
... right angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ; and therefore , AH = AC . But by the last proposition ...
... right angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ; and therefore , AH = AC . But by the last proposition ...
Página 20
... angles BGH , GHD are equal ( by Hyp . ) to two right angles , and AGH , BGH , are also equal ( 6. 1. ) to two right angles , the angles AGH , BGH are equal to the angles BGH , E A G B C H D F GHD : Take away the common angle BGH ...
... angles BGH , GHD are equal ( by Hyp . ) to two right angles , and AGH , BGH , are also equal ( 6. 1. ) to two right angles , the angles AGH , BGH are equal to the angles BGH , E A G B C H D F GHD : Take away the common angle BGH ...
Página 21
... right angles . SCHOLIUM . The angles just spoken of , when compared with each other , assume dif- ferent names . BGH , GHD , we have already named interior angles on the same side ; AGH , GEC , have the same name ; AGH , GHD , are ...
... right angles . SCHOLIUM . The angles just spoken of , when compared with each other , assume dif- ferent names . BGH , GHD , we have already named interior angles on the same side ; AGH , GEC , have the same name ; AGH , GHD , are ...
Página 22
... angles ; therefore AB is pa- rallel ( 19. 1. ) to CD . F A G B E H K D PROP . XXIV . THEOR . Two angles are equal if ... right angles . PROP . XXV . THEOR . If a side of any triangle be produced , the exterior angle is equal to the two ...
... angles ; therefore AB is pa- rallel ( 19. 1. ) to CD . F A G B E H K D PROP . XXIV . THEOR . Two angles are equal if ... right angles . PROP . XXV . THEOR . If a side of any triangle be produced , the exterior angle is equal to the two ...
Página 23
... angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal ( 6. 1. ) to two right ...
... angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal ( 6. 1. ) to two right ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore