## Elements of Geometry |

### From inside the book

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Page 90

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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 91

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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 , which is the same thing , or , OB : CA ::**circ**. OB : a ... Page 92

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**circ**. CA. Fig . 167 If 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 the ... Page 93

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**circ**. CA ;**circ**. CA2 ′′ × CA. or hence Multiplying each member by CA , we have or ¿ CA ×**circ**. CA = « × CÅ , surf . CA = « × CÂ ; therefore , the surface of a circle is equal to the product of the square of the radius by the constant ... Page 165

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**circ**. — DE . - This property must be reciprocal between the two triangles , since they are described in the same ...**circ**. — BC ,**circ**. - AC ,**circ**.-AB. Indeed , the angle D , for example , has for its measure the arc MI ; but MI + BC ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence