New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 14
... angles ; for their sum is equal to that of the two adjacent angles , BAC , CA F. THEOREM ІІ . 38. If one straight line meets two other straight lines at a common point , making adjacent angles , which together are equal to two right angles ...
... angles ; for their sum is equal to that of the two adjacent angles , BAC , CA F. THEOREM ІІ . 38. If one straight line meets two other straight lines at a common point , making adjacent angles , which together are equal to two right angles ...
Page 17
... angle B is equal to the angle E , the side B A will take the direction ED ; therefore the point A will be found some ... BAC to be bisected , or divided into two equal parts , by the straight line A D , making the angle BAD A B D C ...
... angle B is equal to the angle E , the side B A will take the direction ED ; therefore the point A will be found some ... BAC to be bisected , or divided into two equal parts , by the straight line A D , making the angle BAD A B D C ...
Page 21
... angle A greater than D ; B then will the side BC be greater than EF . CE F G Of the two sides DE , DF , let DF be the side which is not shorter than the other ; make the angle EDG equal to BAC ; and make DG equal to AC or DF , and join ...
... angle A greater than D ; B then will the side BC be greater than EF . CE F G Of the two sides DE , DF , let DF be the side which is not shorter than the other ; make the angle EDG equal to BAC ; and make DG equal to AC or DF , and join ...
Page 22
... angle BAC of the one equal to the included angle EDG of the other ; hence the side BC is equal to EG ( Theo . IV . Cor . ) . In the triangle DFG , since DG is equal to DF , the angle DFG is equal to the angle DGF ( Theo . VI ...
... angle BAC of the one equal to the included angle EDG of the other ; hence the side BC is equal to EG ( Theo . IV . Cor . ) . In the triangle DFG , since DG is equal to DF , the angle DFG is equal to the angle DGF ( Theo . VI ...
Page 28
... angles BAC , ACE are equal ( Theo . XVII . ) . Again , let the side BC be produced toward D , and since BD meets two parallels A B , EC , the exterior angle ECD is equal to the interior and opposite angle ABC . But the angle ACE is equal to ...
... angles BAC , ACE are equal ( Theo . XVII . ) . Again , let the side BC be produced toward D , and since BD meets two parallels A B , EC , the exterior angle ECD is equal to the interior and opposite angle ABC . But the angle ACE is equal to ...
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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.