Elements of Geometry and Trigonometry |
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Page 35
... middle term is said to be a mean proportional between the other two . 5. Magnitudes are said to be in proportion by inversion , or inversely , when the consequents are taken as antecedents , and the antecedents as consequents . 6 ...
... middle term is said to be a mean proportional between the other two . 5. Magnitudes are said to be in proportion by inversion , or inversely , when the consequents are taken as antecedents , and the antecedents as consequents . 6 ...
Page 45
... middle point D , of the chord AB , and the middle point G , of the arc subtended by this chord , are three points of the same line perpendicular to the chord . But two points are sufficient to determine the position of a straight line ...
... middle point D , of the chord AB , and the middle point G , of the arc subtended by this chord , are three points of the same line perpendicular to the chord . But two points are sufficient to determine the position of a straight line ...
Page 48
... middle of the arc MHP , and of the arc NHQ ( Prop . VI . ) ; therefore , we shall have the arc MH - HP , and the arc NH = H DIN G QE M F PB HQ ; and therefore MH - NH = HP - HQ ; in other words , MN = PQ . D M Second . When , of the two ...
... middle of the arc MHP , and of the arc NHQ ( Prop . VI . ) ; therefore , we shall have the arc MH - HP , and the arc NH = H DIN G QE M F PB HQ ; and therefore MH - NH = HP - HQ ; in other words , MN = PQ . D M Second . When , of the two ...
Page 49
... middle of this chord , it will pass through each of the two centres C and D ( Prop . VI . Sch . ) . But no more than one straight line can be drawn through two points ; hence the straight line , which passes through the centres , will ...
... middle of this chord , it will pass through each of the two centres C and D ( Prop . VI . Sch . ) . But no more than one straight line can be drawn through two points ; hence the straight line , which passes through the centres , will ...
Page 57
... middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line DE must itself be that perpendicular , which divides AB into two equal parts at the point C. 8 PROBLEM II . At a ...
... middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line DE must itself be that perpendicular , which divides AB into two equal parts at the point C. 8 PROBLEM II . At a ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex