Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 49
Page iii
... means of the diagrams employed in their demonstration . This departure from the method of EUCLID is much to be regretted . The propositions of Geometry are general truths , and ought to be stated in general terms , without reference to ...
... means of the diagrams employed in their demonstration . This departure from the method of EUCLID is much to be regretted . The propositions of Geometry are general truths , and ought to be stated in general terms , without reference to ...
Page 51
... means , and the fourth term , a fourth proportional to the other three . When the second term is equal to the third , it ... mean proportional between A and C , and C is a third proportional to A and B. 5. Quantities are in proportion by ...
... means , and the fourth term , a fourth proportional to the other three . When the second term is equal to the third , it ... mean proportional between A and C , and C is a third proportional to A and B. 5. Quantities are in proportion by ...
Page 52
... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal to the product of two other quantities , two of them may be made the means , and the other two the extremes of a ...
... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal to the product of two other quantities , two of them may be made the means , and the other two the extremes of a ...
Page 119
... mean propor- tional between the hypothenuse and the adjacent segment : 3. The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the right ...
... mean propor- tional between the hypothenuse and the adjacent segment : 3. The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the right ...
Page 120
... mean pro- portional between BC and BD ; and AC will be a mean propor- . tional between CB and CD . For , the triangles ADB and BAC being similar , their homo- logous sides are proportional : hence , B D BC AB :: AB : BD . In like manner ...
... mean pro- portional between BC and BD ; and AC will be a mean propor- . tional between CB and CD . For , the triangles ADB and BAC being similar , their homo- logous sides are proportional : hence , B D BC AB :: AB : BD . In like manner ...
Other editions - View all
Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence