Elements of Geometry |
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Page 7
... drawn through this point and any point of the common line will lie in both planes . Lines may therefore be drawn through this point so as to reach every point of both planes ; in which case the two planes would have every point in ...
... drawn through this point and any point of the common line will lie in both planes . Lines may therefore be drawn through this point so as to reach every point of both planes ; in which case the two planes would have every point in ...
Page 14
... drawing , for the purpose of erecting perpen- diculars at any points of a line ; and , as we shall see in the next ... drawn to the line . ( a ) Since at any point of a line a perpendicular can be erected to the line ( § 13 ) , we may ...
... drawing , for the purpose of erecting perpen- diculars at any points of a line ; and , as we shall see in the next ... drawn to the line . ( a ) Since at any point of a line a perpendicular can be erected to the line ( § 13 ) , we may ...
Page 15
... drawn through A that should be perpendic- ular to BC , let AE repre- sent it . On the FA , lay off FD = AF , and draw DE . P A B FIG . 18 . AE and DE will intersect and have but one point in common by the direction axiom . If AE is a ...
... drawn through A that should be perpendic- ular to BC , let AE repre- sent it . On the FA , lay off FD = AF , and draw DE . P A B FIG . 18 . AE and DE will intersect and have but one point in common by the direction axiom . If AE is a ...
Page 19
... drawn our conclusions without putting any limitations upon the triangle . Any triangle might have the same method applied to it with exactly the same result . We are then not drawing general conclusions from special cases . Exercises ...
... drawn our conclusions without putting any limitations upon the triangle . Any triangle might have the same method applied to it with exactly the same result . We are then not drawing general conclusions from special cases . Exercises ...
Page 20
... drawing . Hint . - Draw an 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 ...
... drawing . Hint . - Draw an 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 ...
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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.