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 14
... greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and ... greater than the angle ECF ; therefore the angle ECD , that is ACD , is greater than BAE : In the same manner , if the ...
... greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and ... greater than the angle ECF ; therefore the angle ECD , that is ACD , is greater than BAE : In the same manner , if the ...
Side 15
... greater than the angle BCA . A D Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) than the interior and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD , be ...
... greater than the angle BCA . A D Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) than the interior and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD , be ...
Side 16
... greater than CA , and BC , CA greater than AB . SCHOLIUM . BC This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ; therefore BC is less than BA + AC , or ...
... greater than CA , and BC , CA greater than AB . SCHOLIUM . BC This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ; therefore BC is less than BA + AC , or ...
Side 17
... greater than the angle EGF ; therefore the angle DFG is greater than EGF ; and much more is the angle EFG greater than the angle EGF ; and because the angle EFG of the triangle EFG is greater than its angle EGF , and because the greater ...
... greater than the angle EGF ; therefore the angle DFG is greater than EGF ; and much more is the angle EFG greater than the angle EGF ; and because the angle EFG of the triangle EFG is greater than its angle EGF , and because the greater ...
Side 18
... greater side is opposite to the greater angle ( Th . 12. ) ; therefore , the side AD is greater than the side AC . COR . 1. The perpendicular measures the true distance of a point from a line , because it is shorter than any other ...
... greater side is opposite to the greater angle ( Th . 12. ) ; therefore , the side AD is greater than the side AC . COR . 1. The perpendicular measures the true distance of a point from a line , because it is shorter than any other ...
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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