Elements of Geometry: With Practical Applications to Mensuration |
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Page 25
... half of ABF , is shorter than A C , the half of A CF ; hence the perpendicular is shorter than any oblique line . Secondly . If BE is equal to B C , then , since A B is common to the triangles , A BE , ABC , and the angles ABE , ABC are ...
... half of ABF , is shorter than A C , the half of A CF ; hence the perpendicular is shorter than any oblique line . Secondly . If BE is equal to B C , then , since A B is common to the triangles , A BE , ABC , and the angles ABE , ABC are ...
Page 63
... half of A B , is equal to the side D G , the half of DE ; therefore the triangles are equal , and CF is equal to CG ( Prop . XIX . Bk . I. ) ; hence the two equal chords A B , DE are equally distant from the centre . Conversely , if the ...
... half of A B , is equal to the side D G , the half of DE ; therefore the triangles are equal , and CF is equal to CG ( Prop . XIX . Bk . I. ) ; hence the two equal chords A B , DE are equally distant from the centre . Conversely , if the ...
Page 72
... half of the arc BD . First . Suppose the centre of the circle C to lie within the angle BAD . Draw the diameter A E ... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC and CAD together , or B ...
... half of the arc BD . First . Suppose the centre of the circle C to lie within the angle BAD . Draw the diameter A E ... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC and CAD together , or B ...
Page 73
... half of the same arc , BOC . 202. Cor . 2. Every angle , BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circumference , BOD ; B that is , by the fourth part of the whole circumference ...
... half of the same arc , BOC . 202. Cor . 2. Every angle , BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circumference , BOD ; B that is , by the fourth part of the whole circumference ...
Page 74
... half the arc FDB ( Prop . XVIII . ) ; that is , by half the arc D B , plus half the arc FD . Hence , since FD is equal to A C , the angle DEB , or its equal angle A EC , is measured by half the sum of the intercepted arcs D B and AC ...
... half the arc FDB ( Prop . XVIII . ) ; that is , by half the arc D B , plus half the arc FD . Hence , since FD is equal to A C , the angle DEB , or its equal angle A EC , is measured by half the sum of the intercepted arcs D B and AC ...
Other editions - View all
Elements of Geometry: With Practical Applications to Mensuration Benjamin Greenleaf No preview available - 2016 |
Elements of Geometry; with Practical Applications to Mensuration Benjamin Greenleaf No preview available - 2012 |
Common terms and phrases
ABCD adjacent angles altitude angle ACB base bisect centre chord circumference circumscribed cone convex surface cylinder diagonal diameter divided draw the straight edges equal angles equal Prop equiangular equilateral triangle equivalent exterior angle four right angles frustum given straight line gles greater homologous homologous sides hypothenuse inches inscribed circle interior angles intersection isosceles less Let ABC line A B line CD mean proportional measured by half multiplied number of sides parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron prism Prob PROBLEM PROPOSITION pyramid quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area right angles Prop right-angled triangle Scholium secant line segment side A B similar slant height sphere spherical polygon spherical triangle square described tangent THEOREM triangle ABC vertex
Popular passages
Page 59 - 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 101 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 37 - 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 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles triangle, in which the side AB is equal to the side AC ; then will the angle B be equal to the angle C.
Page 36 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 121 - 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 166 - ... the same, or a like inclination to one another, which two other planes have, when the said angles of inclination are equal to one another.
Page 168 - 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 272 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...