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 TrigonometryW. E. Dean, 1840 - 317 σελίδες |
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Σελίδα 6
... parallel lines ) , is the sign of equality ; thus , A = B , implies that the quantity denoted by A is equal to the quantity denoted by B , and is read A equal to B. = 19. To signify that A is greater than B , the expression A7B is used ...
... parallel lines ) , is the sign of equality ; thus , A = B , implies that the quantity denoted by A is equal to the quantity denoted by B , and is read A equal to B. = 19. To signify that A is greater than B , the expression A7B is used ...
Σελίδα 11
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2 ...
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2 ...
Σελίδα 27
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
Σελίδα 28
... parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
... parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
Σελίδα 29
... parallel , and since they do not meet towards L and D , they must meet if produced towards K and C. COR . 2. If BGH ... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF ; AB is ...
... parallel , and since they do not meet towards L and D , they must meet if produced towards K and C. COR . 2. If BGH ... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF ; AB is ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore