Elements of Geometry and Trigonometry |
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Page 30
Adrien Marie Legendre. Cor . 2. If two angles of one triangle are respectively equal to ... triangle have more than one obtuse angle . Cor . 4. In every right angled ... ABC , the exterior angle BAD is equal to the sum of the two interior ...
Adrien Marie Legendre. Cor . 2. If two angles of one triangle are respectively equal to ... triangle have more than one obtuse angle . Cor . 4. In every right angled ... ABC , the exterior angle BAD is equal to the sum of the two interior ...
Page 54
... triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the angle CAB is equal to ABC ; hence the angle BCE is double of BAC . Since BCE lies at ...
... triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the angle CAB is equal to ABC ; hence the angle BCE is double of BAC . Since BCE lies at ...
Page 63
... triangle ABC shall be inscribed . PROBLEM XIV . Through a given point , to draw BOOK III . 63.
... triangle ABC shall be inscribed . PROBLEM XIV . Through a given point , to draw BOOK III . 63.
Page 64
... triangle . B Let ABC be the given triangle . Bisect the angles A and B , by the lines AO and BO , meeting in the point 0 ; from the point O , D let fall the perpendiculars OD , OE , OF , on the three sides of the triangle : these ...
... triangle . B Let ABC be the given triangle . Bisect the angles A and B , by the lines AO and BO , meeting in the point 0 ; from the point O , D let fall the perpendiculars OD , OE , OF , on the three sides of the triangle : these ...
Page 65
... triangles AOD , AOF ; and the angles adjacent to the equal side are equal : hence the triangles themselves are . equal ... triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and the same ...
... triangles AOD , AOF ; and the angles adjacent to the equal side are equal : hence the triangles themselves are . equal ... triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and the same ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex