Key to Exercises in EuclidMacmillan and Company, 1880 - 114 páginas |
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Página 5
... Suppose A the given point through which the straight line is to be drawn , and B and C the other given points from which perpendiculars are to be drawn . Join BC , and bisect it at D ; join AD : this shall be the required straight line ...
... Suppose A the given point through which the straight line is to be drawn , and B and C the other given points from which perpendiculars are to be drawn . Join BC , and bisect it at D ; join AD : this shall be the required straight line ...
Página 6
... suppose that AE bisects the angle DAC , and that it is parallel to BC : then will ABC be an isosceles triangle . For since AE is parallel to BC the angle DAE is equal to the angle ABC , by I. 29 , and also the angle CAE is equal to the ...
... suppose that AE bisects the angle DAC , and that it is parallel to BC : then will ABC be an isosceles triangle . For since AE is parallel to BC the angle DAE is equal to the angle ABC , by I. 29 , and also the angle CAE is equal to the ...
Página 9
... suppose the angle ABC equal to the sum of the other two angles ; then twice the angle ABC is equal to the sum of the angles ABC , BCA , CAB , that is equal to two right angles : therefore the angle ABC is a right angle . Lastly , suppose ...
... suppose the angle ABC equal to the sum of the other two angles ; then twice the angle ABC is equal to the sum of the angles ABC , BCA , CAB , that is equal to two right angles : therefore the angle ABC is a right angle . Lastly , suppose ...
Página 13
... Suppose A to be between the parallel straight lines . Through A draw a straight line perpendicular to one of the parallel straight lines , and therefore also perpendicular to the other by I. 29. Let this straight line meet LM at B , and ...
... Suppose A to be between the parallel straight lines . Through A draw a straight line perpendicular to one of the parallel straight lines , and therefore also perpendicular to the other by I. 29. Let this straight line meet LM at B , and ...
Página 14
... Suppose AB less than DC ; from A draw a straight line parallel to BC , meeting DC at E. Then ABCE is a parallelogram . There- fore the angle ABC is equal to the angle AEC , and the side AE is equal to the side BC , I. 34. Therefore AD ...
... Suppose AB less than DC ; from A draw a straight line parallel to BC , meeting DC at E. Then ABCE is a parallelogram . There- fore the angle ABC is equal to the angle AEC , and the side AE is equal to the side BC , I. 34. Therefore AD ...
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Términos y frases comunes
ABCD AC and BD AC is equal angle ABC angle ACB angle BAC angle CAB bisects the angle Cambridge centre chord circle described circumference Crown 8vo describe a circle diameter draw a straight Edition equal to BC equal to four equal to half equal to twice equiangular Euclid Exercise 176 Extra fcap fcap fore given circle given point given straight line greater half a right half the angle Hence Let ABC meeting BC middle point Owens College parallel to BC parallelogram perpendicular plane Professor quadrilateral radius equal rectangle rhombus right angles segment shewn side BC square on BC straight line parallel suppose tangent touch the circle triangle ABC twice the angle twice the rectangle twice the squares
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