## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 45

Page 35

...

...

**proportional**quantities , the first and third are called the antecedents , and the second and fourth the conse- quents ; and the last is said to be a fourth**proportional**to the other three taken in order . 4. Three quantities are in ... Page 36

...

...

**proportional**quantities ( Def . 4. ) , the product of the extremes will be equal to the square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will ... Page 37

Adrien Marie Legendre. PROPOSITION IV . THEOREM . If there be four

Adrien Marie Legendre. PROPOSITION IV . THEOREM . If there be four

**proportional**quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be**proportional**. Let M : N :: P : Q ... Page 38

...

...

**proportional**quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , the four resulting quantities will be**proportional**. Let M , N , P , Q , be the numerical ... Page 39

...

...

**proportional**. Let For , since And since Therefore , or , hence M : NP : Q , and let also M : P :: m : n , then will M : Р : : N ± m : Q ± n . M : NP : Q , M × Q = NxP . M : P :: m : n , Mxn = Pxm MxQMxn = NxP ± Pxm Mx ( Q ± n ) = P ...### Other editions - View all

### 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