## Elements of Geometry and Trigonometry |

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Page 12

A

A

**scholium**is a remark on one or several preceding propositions , which tends to point out their connexion , their use , their restriction , or their extension . A hypothesis is a supposition , made either in the enunciation of a ... Page 16

**Scholium**. The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the ... Page 17

**Scholium**. Two triangles are said to be equal , when being applied to each other , they will exactly coincide ( Ax . 13. ) . Hence , equal triangles have their like parts equal , each to each , since those parts must coincide with each ... Page 19

B E E

B E E

**Scholium**. Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of the triangle EDF , each to each , while the third side BC of the first triangle is greater than the third side EF of the second ... Page 20

**Scholium**. It may be observed that the equal angles lie opposite the equal sides : thus , the equal angles D and A , lie opposite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle , the angles opposite the ...### What people are saying - Write a review

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### Other editions - View all

Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding Cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM produced Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole