## 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 opposite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle the angles opposite to the equal sides ... Page 10

Adrien Marie Legendre. 47.

Adrien Marie Legendre. 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 drawn from the ... 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 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