## Chauvenet's Treatise on Elementary Geometry |

### From inside the book

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Page 65

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**ratio**of A to B is B To find the**ratio**of one quantity to another is , then , to find how many times the first contains the second ; therefore , it is the same thing as to measure the first by the second taken as the unit ( 42 ) . It ... Page 66

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**ratio**. by D 45. Definition . Two quantities are incommensurable when they have no common measure . The**ratio**of two such quantities is called an incommensurable**ratio**. If A and B are two incommensurable quantities , their**ratio**is ... Page 67

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**ratio**is 17 5 • 47. When the preceding process is applied to two quantities and no remainder can be found which is ...**ratio**cannot be exactly expressed by any number whole or fractional . 48. But although an incommensurable**ratio**... Page 68

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**ratios**n m sion , say n B B have the same approximate numerical expres- m , each**ratio**exceeding by a quantity less than n then , these**ratios**cannot differ from each other by so much as 1 n N 1 n But the measure may be assumed as small ... Page 69

William Chauvenet. 50. Definition . A proportion is an equality of

William Chauvenet. 50. Definition . A proportion is an equality of

**ratios**. Thus , if the**ratio**A B A ' is equal to the**ratio**the equality B ' A A ' B B ' is a proportion . It may be read : "**Ratio**of A to B equals**ratio**of A ' to B ...### Other editions - View all

### Common terms and phrases

ABCD adjacent angles allel angle AOB angle BAC angles are equal apothem arc AC BC² bisector bisects called centre chord circum circumference coincide Corollary Definition diagonals diameter dicular distance divided draw equal angles equally distant exterior angle ference figure four right angles geometry given angle given point given straight line greater hence homologous sides hypotenuse inscribed inscribed angle intercepted arcs less Let ABC measured by one-half middle point number of sides oblique lines one-half the arc opposite sides parallel to BC parallelogram pendicular perimeter perpen perpendicular points of intersection produced proportion PROPOSITION quadrilateral quantities radii radius ratio rectangle regular polygon rhombus right angles right triangles Scholium secant line segment semi-circumference side AC sides are equal square straight line drawn symmetrical with respect tangent theorem triangle ABC triangles are equal vertex

### Popular passages

Page 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 31 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP

Page 201 - Words, Facts, and Phrases : A Dictionary of Curious, Quaint, and Out-of-the-Way Matters. By ELIEZER EDWARDS.

Page 120 - Any side of a spherical triangle is less than the sum of the other two.

Page 81 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.

Page 92 - Every point in the bisector of an angle is equally distant from the sides of the angle...

Page 58 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.