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 sider |
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Side 9
... angle in the one , equal to two sides and the included angle in the other ... ACB . to DFE . AA For , if the triangle ABC be applied to the triangle DEF ... angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide ...
... angle in the one , equal to two sides and the included angle in the other ... ACB . to DFE . AA For , if the triangle ABC be applied to the triangle DEF ... angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide ...
Side 10
... angles at the base of an isosceles triangle are equal to one another : namely , those to which the equal sides are opposite . If the triangle ABC have the side AC equal to the side BC : then will the angle ... ACB ; the side AB is also equal ...
... angles at the base of an isosceles triangle are equal to one another : namely , those to which the equal sides are opposite . If the triangle ABC have the side AC equal to the side BC : then will the angle ... ACB ; the side AB is also equal ...
Side 11
... ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the ...
... ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the ...
Side 12
... angles BAC , BGC , also equal , the two triangles BAC , BGC or EDF , are identical ( Th . 1. ) and have the other angles equal ; namely , the angle ABC equal to GBC , and the angle ACB equal to the angle GCB . PROP . VI . THEOR . The angles ...
... angles BAC , BGC , also equal , the two triangles BAC , BGC or EDF , are identical ( Th . 1. ) and have the other angles equal ; namely , the angle ABC equal to GBC , and the angle ACB equal to the angle GCB . PROP . VI . THEOR . The angles ...
Side 14
... ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 6.1 . ) to two right angles : there- fore the angles ABC , BCA are less than ... angle ABC is also greater than the 14 ELEMENTS.
... ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 6.1 . ) to two right angles : there- fore the angles ABC , BCA are less than ... angle ABC is also greater than the 14 ELEMENTS.
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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