Elements of Geometry |
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Page 20
... auxiliary line connecting two points of inter- section and then apply Ex . 1. Two applications will be necessary . 3. Establish the theorem when the third and fourth lines intersect between the first and second . NOTE . In order to ...
... auxiliary line connecting two points of inter- section and then apply Ex . 1. Two applications will be necessary . 3. Establish the theorem when the third and fourth lines intersect between the first and second . NOTE . In order to ...
Page 23
... auxiliary line MN be drawn perpendicular to AB ( § 13 ) it will be perpendicular to DC ( § 19 , Ex . 1 ) . But we do not as yet know whether it will bisect DC or not . If we revolve the portion of the figure that lies on the right of ...
... auxiliary line MN be drawn perpendicular to AB ( § 13 ) it will be perpendicular to DC ( § 19 , Ex . 1 ) . But we do not as yet know whether it will bisect DC or not . If we revolve the portion of the figure that lies on the right of ...
Page 27
... auxiliary line AE . By $ 20 , Ex . 2 , the line CB will be the perpendicular bisector of the segment AE . BD ( r ) E K FIG . 25 . If the figures to the right of the line CK be revolved on CK as an axis , the point E will fall at A ; the ...
... auxiliary line AE . By $ 20 , Ex . 2 , the line CB will be the perpendicular bisector of the segment AE . BD ( r ) E K FIG . 25 . If the figures to the right of the line CK be revolved on CK as an axis , the point E will fall at A ; the ...
Page 38
... auxiliary line DB . It will separate the angle to which it is drawn into two parts , one of which equals the CAB . The B is the larger . AC AD + DC = BD + DC > BC . Exercises . line . ― = Q. E. D. -1 . Prove the same by using AE as an ...
... auxiliary line DB . It will separate the angle to which it is drawn into two parts , one of which equals the CAB . The B is the larger . AC AD + DC = BD + DC > BC . Exercises . line . ― = Q. E. D. -1 . Prove the same by using AE as an ...
Page 40
... each other , and the segments AB and AF would be equal . If the auxiliary line BF were drawn , AP would be a perpendicular bisector to it . This determination of relations that would exist if the angle 40 ELEMENTS OF GEOMETRY .
... each other , and the segments AB and AF would be equal . If the auxiliary line BF were drawn , AP would be a perpendicular bisector to it . This determination of relations that would exist if the angle 40 ELEMENTS OF GEOMETRY .
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Common terms and phrases
AB² altitude Analysis apothem approach auxiliary line axis base bisect called centre chord circumference circumscribed polygon coincide cone convex convex polygon corresponding lines curve cylinder decagon determine diagonals diameter dicular diedral distance ellipse equally distant figure Find the locus fixed point frustum Geometry given circle given line given point given segment greater Hence hypothenuse inscribed polygon interior angles isosceles joining lines be drawn middle point move NOTE number of sides oblique parabola parallel parallelogram parallelopiped pass perimeter perpen perpendicular bisector point of intersection position prism PROBLEM pyramids Q. E. D. Exercises quadrangle radii radius ratio re-entrant polygon rectangle regular polygon represent right angles right circular cone right triangle rotation secant Show side opposite similar sphere spherical triangle square subtended surface THEOREM three sides triangular prism triedral vertex vertices volume
Popular passages
Page 25 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 26 - If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal.