Elementary GeometryJ.B. Lippincott Company, 1893 |
From inside the book
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Page 14
... included between the points of intersection ; viz . , AB , BC , CA. The angles of the triangle are the angles formed by the sides with each other ; viz . , CAB , ABC , BCA . The three angular points , A , B , C , which are the vertices ...
... included between the points of intersection ; viz . , AB , BC , CA. The angles of the triangle are the angles formed by the sides with each other ; viz . , CAB , ABC , BCA . The three angular points , A , B , C , which are the vertices ...
Page 20
... angle BOC , and hence they are equal ( 16 ) . In like manner it can be proved that the opposite angles AOD and BOC ... included angle of the one are respectively equal to two sides and the included angle of the other . In the triangles ...
... angle BOC , and hence they are equal ( 16 ) . In like manner it can be proved that the opposite angles AOD and BOC ... included angle of the one are respectively equal to two sides and the included angle of the other . In the triangles ...
Page 22
... angle BAC , and meeting the side BC at D. A B D 0 In the triangles ABD and ACD the side AB is equal to the side AC by hypothesis , the side AD is common , and the included angle BAD is equal to the included angle CAD by construction ...
... angle BAC , and meeting the side BC at D. A B D 0 In the triangles ABD and ACD the side AB is equal to the side AC by hypothesis , the side AD is common , and the included angle BAD is equal to the included angle CAD by construction ...
Page 23
... angle EGF . The two triangles EDF and EGF have now the side ED equal to the side EG by hypothesis , the side DF equal to the side FG by hypothesis , and the included angle EDF proved equal to the included angle EGF . Hence the tri ...
... angle EGF . The two triangles EDF and EGF have now the side ED equal to the side EG by hypothesis , the side DF equal to the side FG by hypothesis , and the included angle EDF proved equal to the included angle EGF . Hence the tri ...
Page 24
... included angle ACD equal to the included angle ACB , since they are adjacent angles and ACB is a right angle by hypothesis , are equal , by Proposition VI . In like manner the triangle A'D'C ' may be proved equal to the triangle A'B'C ...
... included angle ACD equal to the included angle ACB , since they are adjacent angles and ACB is a right angle by hypothesis , are equal , by Proposition VI . In like manner the triangle A'D'C ' may be proved equal to the triangle A'B'C ...
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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.