## Elements of Geometry and Trigonometry |

### From inside the book

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Page 30

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**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

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**divided**into M number of units , each equal to A ' : then A = M × 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

... proportional , when one of them is pro- portional to unity

... proportional , when one of them is pro- portional to unity

**divided**by the other , in which case their pro- duct is always equal to a constant quantity . PROPOSITION I. THEOREM . When four quantities are in proportion BOOK II . 35. Page 52

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**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

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 ...### Other editions - View all

### 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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex