A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry

J.B. Lippincott, 1871 - 368 sivua

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Sivu 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
Sivu 129 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Sivu 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Sivu 115 - It follows from § 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Sivu 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Sivu 216 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Sivu 74 - An angle formed by a tangent and a chord is measured by onehalf the intercepted arc.
Sivu 107 - If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon AB...
Sivu 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Sivu 255 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

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