## Elements of Geometry |

### From inside the book

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Page 88

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**circ**. CA and**circ**. OB ( fig . 165 ) , the circumferences of the circles whose radii are CA and OB , we say that**circ**. CA :**circ**. OB :: CA : OB . For , if this proportion be not true , CA will be to OB as**circ**. CA is to a fourth ... Page 89

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**circ**. CA is to a circumference greater than**circ**. OB ; for , if this were the case , we should have by inversion , OB CA : a circumference greater than**circ**. OB :**circ**. CA , or , which is the same thing , OB : CA :**circ**. OB : a ... Page 90

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**circ**. CA. Fig . 167. If 1⁄2 CA ×**circ**. CA ( fig . 167 ) be not the area of the circle of which CA is the radius , this quantity will be the measure of a circle either greater or less . Let us suppose , in the first place , that it is ... Page 91

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**circ**. CA ; or hence**circ**. CA 2π × CA. Multiplying each member by CA , we have or CA ×**circ**. CA = π × CA , 2 surf . CAX CA ; therefore , the surface of a circle is equal to the product of the square of the radius by the constant ... Page 163

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**circ**. - BC ,**circ**. AC ,**circ**. AB . Indeed , the angle D , for example , has for its measure the arc MI ; but - MI + BC = MC + BI = 1⁄2**circ**.; therefore the arc MI , the measure of the angle D , = 1**circ**. — BC , and so of the others ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence