## Elements of Geometry and Trigonometry |

### From inside the book

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**centre**. The circle is the space terminated by A this curved line . * 2. Every straight line , CA , CE , CD , drawn from the**centre**to the circum- ference , is called a radius or semidiam- F H eter ; every line which , like AB , passes ... Page 42

... , otherwise there would , in the one or the other , be points unequally dis- tant from the

... , otherwise there would , in the one or the other , be points unequally dis- tant from the

**centre**, which is contrary to the definition of a circle . 1 PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY . Page 43

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**centre**; and hence , there would be three equal straight lines drawn from the same point to the same straight line , which is impossible ( Book 1. Prop . XV . Cor . 2. ) . PROPOSITION IV . THEOREM . In the same circle , or in equal ... Page 45

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**centre**of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the**centre**on the same chord , since both of them pass through the**centre**and middle of the ... Page 46

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**centre**O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we say farther , that ...### 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