## Elements of Geometry |

### From inside the book

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**Scholium**is a remark upon one or more propositions which have gone before , tending to show their connexion , their restric- tion , their extension , or the manner of their application . A Hypothesis is a supposition made either in the ... Page 6

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**Scholium**. The four angles , formed about a point by two straight lines which cut each other , are together equal to four right angles ; for the angles ACE , BCE , taken together , are equal to two right angles ; also the other angles ... Page 9

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**Scholium**. It may be remarked , that equal angles are opposite to equal sides ; thus , the equal angles A and D are op- posite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal ... Page 10

Adrien Marie Legendre. Fig . 29 . - 47.

Adrien Marie Legendre. Fig . 29 . - 47.

**Scholium**. From the equality of the triangles ABD , ACD , it follows , that the angle BAD DAC , and that the angle BDA ADC ; therefore these two last are right angles . Hence a straight line ... Page 11

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**Scholium**. Through the same point C ( fig . 17 ) , in the Fig . 17 . line AB , it is also impossible to draw two perpendiculars to that line ; for , if CD and CE were these two perpendiculars , the an- gle DCB would be a right angle as ...### 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