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
... PROP . XIX . THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines ...
... PROP . XIX . THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines ...
Página 21
... PROP . XXII . THEOR . If a straight line , cutting two other lines , make the sum of the two interior angles on the same side , less than two right angles , those two lines will meet if produced . Let the straight line EF ( see last ...
... PROP . XXII . THEOR . If a straight line , cutting two other lines , make the sum of the two interior angles on the same side , less than two right angles , those two lines will meet if produced . Let the straight line EF ( see last ...
Página 25
... PROP . XXVII . THEOR . The straight lines which join the extremities of two equal and parallel straight lines , towards the same parts , are also themselves equal and parallel . Let AB , CD , be equal and parallel straight lines , and ...
... PROP . XXVII . THEOR . The straight lines which join the extremities of two equal and parallel straight lines , towards the same parts , are also themselves equal and parallel . Let AB , CD , be equal and parallel straight lines , and ...
Página 27
... PROP . XXX . THEOR . Parallelograms upon equal bases , and between the same parallels , are equivalent to one another . Let ABCD , EFGH be parallelograms upon equal bases BC , FG , and between the same parallels AH , BG ; the ...
... PROP . XXX . THEOR . Parallelograms upon equal bases , and between the same parallels , are equivalent to one another . Let ABCD , EFGH be parallelograms upon equal bases BC , FG , and between the same parallels AH , BG ; the ...
Página 28
... PROP . XXXII . THEOR . Triangles upon equal bases , and between the same parallels , are equivalent to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and be- tween the same parallels BF , AD : The triangle ABC ...
... PROP . XXXII . THEOR . Triangles upon equal bases , and between the same parallels , are equivalent to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and be- tween the same parallels BF , AD : The triangle ABC ...
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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