The Elements of Plane and Solid Geometry: With Numerous Exercises |
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Page 158
... triangle , if a perpendicular be drawn from the right angle to the hypotenuse : ( 1 ) The two triangles on each side of it are similar to the whole triangle and to each other . ( 2 ) The perpendicular is a mean proportional between the ...
... triangle , if a perpendicular be drawn from the right angle to the hypotenuse : ( 1 ) The two triangles on each side of it are similar to the whole triangle and to each other . ( 2 ) The perpendicular is a mean proportional between the ...
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Common terms and phrases
ABCD adjacent angles altitude angles are equal base bisect bisector called centre chord circumference circumscribed coincide common cone of revolution Cons construct cylinder diagonals diameter diedral angle distance divided draw equally distant equivalent EXERCISES exterior angle faces feet Find the area Find the volume frustum given circle given line given point given straight line homologous homologous sides hypotenuse inches intersection isosceles triangle lateral area lateral edges Let ABC meet middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced Proposition Proposition 13 pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon right angles segment similar slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetraedron Theorem triangle ABC triangular prism triedral vertex
Popular passages
Page 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 188 - Two triangles having 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.
Page 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Page 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Page 206 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Page 97 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.
Page 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 12 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.