Elements of Geometry and Trigonometry |
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Page 30
... divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general , into as many triangles , less two , as the polygon has sides ; for , these triangles may be considered as having the point A ...
... divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general , into as many triangles , less two , as the polygon has sides ; for , these triangles may be considered as having the point A ...
Page 34
... divided into M number of units , each equal to A ' : then A = Mx A ' : let B be divided into N number of equal units , each equal to A ' ; then B - Nx A ' ; M and N being integral num- bers . Now the ratio of A to B , will be the same ...
... divided into M number of units , each equal to A ' : then A = Mx A ' : let B be divided into N number of equal units , each equal to A ' ; then B - Nx A ' ; M and N being integral num- bers . Now the ratio of A to B , will be the same ...
Page 35
... same ratio as the other diminishes . In such case , either of them is equal to a constant quantity divided by the other , and their product is constant . PROPOSITION I. THEOREM . When four quantities are in proportion BOOK II . 35.
... same ratio as the other diminishes . In such case , either of them is equal to a constant quantity divided by the other , and their product is constant . PROPOSITION I. THEOREM . When four quantities are in proportion BOOK II . 35.
Page 52
... divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will be equal to each of the partial arcs Dr , xy , & c . ( Prop . XV . ) . Therefore the whole arc ...
... divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will be equal to each of the partial arcs Dr , xy , & c . ( Prop . XV . ) . Therefore the whole arc ...
Page 53
Adrien Marie Legendre Charles Davies. AB to be divided into equal parts , each of which is less than DO ; there will be at least one point of division between D and O ; let I be that point ; and draw CI . The arcs AB , AI , will be to ...
Adrien Marie Legendre Charles Davies. AB to be divided into equal parts , each of which is less than DO ; there will be at least one point of division between D and O ; let I be that point ; and draw CI . The arcs AB , AI , will be to ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex