Elements of Geometry and Conic Sections |
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Page 57
... triangle to a rec- tangle , & c . 3. Similar figures are such as have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . Sides which have the same position in the ...
... triangle to a rec- tangle , & c . 3. Similar figures are such as have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . Sides which have the same position in the ...
Page 70
... triangle ABE is isosceles . For , since AD is parallel to EB , the angle ABE is equal to the alternate angle DAB ... similar . Let ABC , DCE be two equiangular triangles , having the angle BAC equal to the angle CDE , and the angle ...
... triangle ABE is isosceles . For , since AD is parallel to EB , the angle ABE is equal to the alternate angle DAB ... similar . Let ABC , DCE be two equiangular triangles , having the angle BAC equal to the angle CDE , and the angle ...
Page 71
... similar . Cor . Two triangles are similar when they have two an gles equal , each to each , for then the third angles must also be equal . Scholium . In similar triangles the homologous sides are opposite to the equal angles ; thus ...
... similar . Cor . Two triangles are similar when they have two an gles equal , each to each , for then the third angles must also be equal . Scholium . In similar triangles the homologous sides are opposite to the equal angles ; thus ...
Page 72
... triangles GEF , DEF have their three sides equal , each to each ; hence their angles also are equal ( Prop . XV . , B. I. ) . But , by con- struction , the triangle GEF is equiangular to the triangle ... triangles are similar , 72 GEOMETRY.
... triangles GEF , DEF have their three sides equal , each to each ; hence their angles also are equal ( Prop . XV . , B. I. ) . But , by con- struction , the triangle GEF is equiangular to the triangle ... triangles are similar , 72 GEOMETRY.
Page 73
Elias Loomis. PROPOSITION XXI . THEOREM . Two triangles are similar , when they have their homologous sides parallel or perpendicular to each other . Let the triangles ABC , abc , DEF have their homologous sides parallel or perpendicular ...
Elias Loomis. PROPOSITION XXI . THEOREM . Two triangles are similar , when they have their homologous sides parallel or perpendicular to each other . Let the triangles ABC , abc , DEF have their homologous sides parallel or perpendicular ...
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Common terms and phrases
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 17 - If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal, each to each.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.