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 13
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exte- rior angle ACD is greater than either of the interior OF GEOMETRY . BOOK 1 . 13.
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exte- rior angle ACD is greater than either of the interior OF GEOMETRY . BOOK 1 . 13.
Página 14
... interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC , and produce AC to G. A F 4 B E D Because AE is equal to EC , and BE to EF ; AE , EB are ...
... interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC , and produce AC to G. A F 4 B E D Because AE is equal to EC , and BE to EF ; AE , EB are ...
Página 15
... interior and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD , be- cause the side AB is equal to the side . AD ; therefore the angle ABD is like- wise greater than the angle ACB ; wherefore much more is the angle ABC greater than ...
... interior and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD , be- cause the side AB is equal to the side . AD ; therefore the angle ABD is like- wise greater than the angle ACB ; wherefore much more is the angle ABC greater than ...
Página 16
... interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
... interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
Página 19
... interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon ...
... interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon ...
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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