Elements of Geometry |
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Page 3
... determining the character of the curve . As any fixed point has a fixed direction from another fixed point , only one straight line can join two points . 4. Our idea of distance involves the ideas of motion DEFINITIONS . 3.
... determining the character of the curve . As any fixed point has a fixed direction from another fixed point , only one straight line can join two points . 4. Our idea of distance involves the ideas of motion DEFINITIONS . 3.
Page 51
... curve is a straight line which intersects the curve . A secant will intersect a curve in two points . The nature of a curve may be such that a secant may intersect it in more than two points . A chord is the segment of a secant between ...
... curve is a straight line which intersects the curve . A secant will intersect a curve in two points . The nature of a curve may be such that a secant may intersect it in more than two points . A chord is the segment of a secant between ...
Page 52
... curve will have at A. A tangent is sometimes said to be the limit toward which the secant approaches as the points ... curves have secants and chords ; but comparatively a small number of curves have centres and diameters . The circle is ...
... curve will have at A. A tangent is sometimes said to be the limit toward which the secant approaches as the points ... curves have secants and chords ; but comparatively a small number of curves have centres and diameters . The circle is ...
Page 132
... ( MM1 ) be drawn , the area included between the curve and PP1 will be exactly equal to the rectangle PQQ1P1 . This fact will be established in § 163 . M F P M1 Q1 P FIG . 168 . 101. By Exs . 5 and 6 , § 94 132 ELEMENTS OF GEOMETRY .
... ( MM1 ) be drawn , the area included between the curve and PP1 will be exactly equal to the rectangle PQQ1P1 . This fact will be established in § 163 . M F P M1 Q1 P FIG . 168 . 101. By Exs . 5 and 6 , § 94 132 ELEMENTS OF GEOMETRY .
Page 135
... curve will be the en- veloping one . Discuss the problem thoroughly . FIG . 170 . A M FIG . 171 . B B 104. Problems . - 1 . To inscribe a regular decagon in a circle . Analysis . — If AB were the side of a regular inscribed decagon ...
... curve will be the en- veloping one . Discuss the problem thoroughly . FIG . 170 . A M FIG . 171 . B B 104. Problems . - 1 . To inscribe a regular decagon in a circle . Analysis . — If AB were the side of a regular inscribed decagon ...
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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.