Elements of Geometry and Trigonometry Translated from the French of A.M. Legendre by David Brewster: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes and Company, 1838 - 359 σελίδες |
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Σελίδα 10
... problem . The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a remark on one or several ...
... problem . The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a remark on one or several ...
Σελίδα 55
... PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS PROBLEM I. To divide a given straight line into two equal parts . Let AB be the given straight line . From the points A and B as centres , with a radius greater than the half of AB ...
... PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS PROBLEM I. To divide a given straight line into two equal parts . Let AB be the given straight line . From the points A and B as centres , with a radius greater than the half of AB ...
Σελίδα 56
... PROBLEM II . At a given point , in a given straight line , to erect a perpendicu- lar to this line . Let A be the given point , and BC the given line . B A Take the points B and C at equal dis- tances from A ; then from the points B and ...
... PROBLEM II . At a given point , in a given straight line , to erect a perpendicu- lar to this line . Let A be the given point , and BC the given line . B A Take the points B and C at equal dis- tances from A ; then from the points B and ...
Σελίδα 57
... PROBLEM V. To divide a given arc , or a given angle , into two equal parts . First . Let it be required to divide the arc AEB into two equal parts . From the points A and B , as centres , with the same radius , describe two arcs cutting ...
... PROBLEM V. To divide a given arc , or a given angle , into two equal parts . First . Let it be required to divide the arc AEB into two equal parts . From the points A and B , as centres , with the same radius , describe two arcs cutting ...
Σελίδα 58
... PROBLEM VI . Through a given point , to draw a parallel to a given straight line . Let A be the given point , and BC the given line . B A E DI From the point A as a centre , with a radius greater than the shortest dis- tance from A to ...
... PROBLEM VI . Through a given point , to draw a parallel to a given straight line . Let A be the given point , and BC the given line . B A E DI From the point A as a centre , with a radius greater than the shortest dis- tance from A to ...
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adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine Cotang 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 middle point number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM trian triangle ABC triangular prism vertex