New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 11
... quadrilateral which has its op- posite sides parallel . 21. A Rectangle is any parallelo- gram whose angles are ... quadrilateral which has only two of its sides parallel ; as the quadrilateral R S T U. A Trapezium is a ...
... quadrilateral which has its op- posite sides parallel . 21. A Rectangle is any parallelo- gram whose angles are ... quadrilateral which has only two of its sides parallel ; as the quadrilateral R S T U. A Trapezium is a ...
Page 29
... quadrilateral is equal to four right angles ; hence , if all the angles of a quadri- lateral are equal , each of them is a right angle ; also , if three of the angles are right angles , the fourth is likewise a right angle . 75. Cor . 2 ...
... quadrilateral is equal to four right angles ; hence , if all the angles of a quadri- lateral are equal , each of them is a right angle ; also , if three of the angles are right angles , the fourth is likewise a right angle . 75. Cor . 2 ...
Page 31
... quadrilateral hav- ing its opposite sides equal ; then will the equal sides be parallel , and the fig- ure be a ... quadrilateral ABCD is a parallelogram . THEOREM XXIV . 83. If two opposite sides of a quadrilateral are equal and ...
... quadrilateral hav- ing its opposite sides equal ; then will the equal sides be parallel , and the fig- ure be a ... quadrilateral ABCD is a parallelogram . THEOREM XXIV . 83. If two opposite sides of a quadrilateral are equal and ...
Page 32
... quadrilateral , hav- ing the sides AB , CD equal and par- allel ; then will the other sides also be equal and parallel . A D C B Draw the diagonal BD ; then , since AB is parallel to CD , and BD meets them , the alternate angles ABD ...
... quadrilateral , hav- ing the sides AB , CD equal and par- allel ; then will the other sides also be equal and parallel . A D C B Draw the diagonal BD ; then , since AB is parallel to CD , and BD meets them , the alternate angles ABD ...
Page 70
... quadrilateral A BED , we take away the tri- angle ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral A BED , we take away the triangle CBE , there will remain the parallelogram ABCD . Hence the ...
... quadrilateral A BED , we take away the tri- angle ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral A BED , we take away the triangle CBE , there will remain the parallelogram ABCD . Hence the ...
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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.