New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 11
... Parallelogram is a quadrilateral which has its op- posite sides parallel . 21. A Rectangle is any parallelo- gram whose angles are right angles ; as the parallelogram ABCD . D C A B H G A Square is a rectangle whose sides are equal ; as ...
... Parallelogram is a quadrilateral which has its op- posite sides parallel . 21. A Rectangle is any parallelo- gram whose angles are right angles ; as the parallelogram ABCD . D C A B H G A Square is a rectangle whose sides are equal ; as ...
Page 12
... equal to either of the other sides . AXIOMS . 26. An Axiom is a self - evident truth ' ; such as , 1. Things which ... parallel to another straight line . 4. That an angle may be described equal to any given angle . PROPOSITIONS ...
... equal to either of the other sides . AXIOMS . 26. An Axiom is a self - evident truth ' ; such as , 1. Things which ... parallel to another straight line . 4. That an angle may be described equal to any given angle . PROPOSITIONS ...
Page 24
... equal to DF , and the side A B equal to DE ; then will the triangle A B C be equal to the triangle DE F. B G D CE F ... parallel . E Let the straight line EF intersect the two straight lines AB , CD , making the alternate angles BGH , I CHG ...
... equal to DF , and the side A B equal to DE ; then will the triangle A B C be equal to the triangle DE F. B G D CE F ... parallel . E Let the straight line EF intersect the two straight lines AB , CD , making the alternate angles BGH , I CHG ...
Page 25
... parallel , let them meet in some point K , and through O , the middle point of GH , draw the straight line IK , making IO equal to OK , and join HI . Then the opposite angles KOG , IO H , formed by the intersection of the two straight ...
... parallel , let them meet in some point K , and through O , the middle point of GH , draw the straight line IK , making IO equal to OK , and join HI . Then the opposite angles KOG , IO H , formed by the intersection of the two straight ...
Page 26
... equal to the angle AGH ; and these are alternate angles ; hence the lines AB , CD are parallel . 63. Cor . If two straight lines are perpendicular to an- other , they are parallel . THEOREM XVII . 64. If a straight line intersects two ...
... equal to the angle AGH ; and these are alternate angles ; hence the lines AB , CD are parallel . 63. Cor . If two straight lines are perpendicular to an- other , they are parallel . THEOREM XVII . 64. If a straight line intersects two ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 29 - 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 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.