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 24
... named convex polygons . Every convex po- F E lygon is such that a straight line , drawn at pleasure , cannot meet the con- tour of the polygon in more than two points . t PROP . XXVII . THEOR . The straight lines 24 ELEMENTS.
... named convex polygons . Every convex po- F E lygon is such that a straight line , drawn at pleasure , cannot meet the con- tour of the polygon in more than two points . t PROP . XXVII . THEOR . The straight lines 24 ELEMENTS.
Página 25
... meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) ; and because AB is equal to CD , and BC com- mon to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to C B D ...
... meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) ; and because AB is equal to CD , and BC com- mon to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to C B D ...
Página 26
... meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) to one another ; and because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD are equal ( 21. 1. ) to one another ; wherefore the two triangles ...
... meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) to one another ; and because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD are equal ( 21. 1. ) to one another ; wherefore the two triangles ...
Página 38
... meet BC at equal distances from the common perpendicular , these triangles would be equal . Secondly . If the given ... meets the two straight lines BC , DF , makes the alternate angles EAD , ADC equal to one another , EF is parallel ...
... meet BC at equal distances from the common perpendicular , these triangles would be equal . Secondly . If the given ... meets the two straight lines BC , DF , makes the alternate angles EAD , ADC equal to one another , EF is parallel ...
Página 40
... meet if produced ( 22. 1. ) : Therefore HB , FE will meet , if pro- duced ; let them meet in K , and through K draw KL parallel to EA or FH , and produce HA , GB to the points L , M : Then HLKF is a parallel- ogram , of which the ...
... meet if produced ( 22. 1. ) : Therefore HB , FE will meet , if pro- duced ; let them meet in K , and through K draw KL parallel to EA or FH , and produce HA , GB to the points L , M : Then HLKF is a parallel- ogram , of which the ...
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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