Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 14
... triangle is a portion of a plane bounded by three intersecting straight lines ; as ABC . The sides of the triangle ... right triangle is one which has a right angle ; as MNP , which is right - angled at N. The side MP , opposite to the ...
... triangle is a portion of a plane bounded by three intersecting straight lines ; as ABC . The sides of the triangle ... right triangle is one which has a right angle ; as MNP , which is right - angled at N. The side MP , opposite to the ...
Page 23
... triangle ABC to be placed so that its base BC coincides with its equal EF , but so that the vertex A F falls on the opposite side of EF from D , as at G , and join D and G by a straight line . The triangle ... right triangles are BOOK I. 23.
... triangle ABC to be placed so that its base BC coincides with its equal EF , but so that the vertex A F falls on the opposite side of EF from D , as at G , and join D and G by a straight line . The triangle ... right triangles are BOOK I. 23.
Page 24
William Chauvenet. PROPOSITION X. - THEOREM . 26. Two right triangles are equal when they have the hypote nuse and a ... triangle ADC and the triangle ABC having the side AC in common ; the side CD equal to the side CB by con- struction ...
William Chauvenet. PROPOSITION X. - THEOREM . 26. Two right triangles are equal when they have the hypote nuse and a ... triangle ADC and the triangle ABC having the side AC in common ; the side CD equal to the side CB by con- struction ...
Page 29
... triangle upon the base bisects the base and bisects the vertical angle . 2. Theorem . - Two right triangles are equal when they have the hypotenuse and an adjacent angle of the one respectively equal to the hypotenuse and an adjacent ...
... triangle upon the base bisects the base and bisects the vertical angle . 2. Theorem . - Two right triangles are equal when they have the hypotenuse and an adjacent angle of the one respectively equal to the hypotenuse and an adjacent ...
Page 38
... triangle is equal to two right angles . Let ABC be any triangle ; then the sum of its three angles is equal to two right angles . Produce BC , and through C draw CE parallel to BA . Since the line AC meets the parallel lines AB and EC ...
... triangle is equal to two right angles . Let ABC be any triangle ; then the sum of its three angles is equal to two right angles . Produce BC , and through C draw CE parallel to BA . Since the line AC meets the parallel lines AB and EC ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - 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 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.