Elements of Geometry |
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Page v
... placed by exercises , every one of which the student must work out as he comes to them . At the end of the Plane Geometry and at the end of the Solid Geometry there will be found a sufficiently large number of exercises to give a review ...
... placed by exercises , every one of which the student must work out as he comes to them . At the end of the Plane Geometry and at the end of the Solid Geometry there will be found a sufficiently large number of exercises to give a review ...
Page 2
... placed near it , and the position of another point by the letter ( B ) , placed near it , the direction ( AB ) is established . The direction of ( B ) from ( A ) and the direction of ( 4 ) from ( B ) are opposites . Relations expressed ...
... placed near it , and the position of another point by the letter ( B ) , placed near it , the direction ( AB ) is established . The direction of ( B ) from ( A ) and the direction of ( 4 ) from ( B ) are opposites . Relations expressed ...
Page 23
... placed before the proof , it is a statement of relations said to exist . The proof is the establishing of these said relations ( see § 17 ) . When placed after the determination of relations it is in the form of a conclusion ( see § 16 ) ...
... placed before the proof , it is a statement of relations said to exist . The proof is the establishing of these said relations ( see § 17 ) . When placed after the determination of relations it is in the form of a conclusion ( see § 16 ) ...
Page 27
... placed that a pair of equal sides shall lie together , and the triangles be not superimposed , we shall have them placed as in figure ( r ) . By the terms of the theo- rem , B and C are two points equally distant from A and E. Draw the ...
... placed that a pair of equal sides shall lie together , and the triangles be not superimposed , we shall have them placed as in figure ( r ) . By the terms of the theo- rem , B and C are two points equally distant from A and E. Draw the ...
Page 28
... placed in like relation to the equal angles . Corresponding sides are often called homologous sides . 24. THEOREM . If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other ...
... placed in like relation to the equal angles . Corresponding sides are often called homologous sides . 24. THEOREM . If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other ...
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Common terms and phrases
ABē 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.