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 16
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less than the other two ... angle EDG equal to the angle BAC : and make DG 16 ELEMENTS.
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less than the other two ... angle EDG equal to the angle BAC : and make DG 16 ELEMENTS.
Página 17
... angle BAC : and make DG equal to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the an- gle BAC is equal to the angle EDG , therefore the ...
... angle BAC : and make DG equal to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the an- gle BAC is equal to the angle EDG , therefore the ...
Página 22
... angle BAC is equal to EDF . For , draw GAD through the vertices . And since AB is parallel to DF , the ex- terior angle GAB is ( 21. 1. ) equal to GDF ; and , for the same reason , GAC is equal to GDE ; there consequently re- mains the ...
... angle BAC is equal to EDF . For , draw GAD through the vertices . And since AB is parallel to DF , the ex- terior angle GAB is ( 21. 1. ) equal to GDF ; and , for the same reason , GAC is equal to GDE ; there consequently re- mains the ...
Página 23
... angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole ex- terior 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 ...
... angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole ex- terior 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 ...
Página 26
... angle of the other ( Th . 2. ) ; viz . the side AB to the side CD , and AC to BD , and the angle BAC equal to the angle BDC . And because the angle ABC is equal to the angle BCD , and the angle CBD to the angle ACB , the whole angle ABD ...
... angle of the other ( Th . 2. ) ; viz . the side AB to the side CD , and AC to BD , and the angle BAC equal to the angle BDC . And because the angle ABC is equal to the angle BCD , and the angle CBD to the angle ACB , the whole angle ABD ...
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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