## Elements of Geometry and Trigonometry |

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**Prop**. 26**Prop**. 33 30**Prop**. 4**Prop**. 5 34 28 288280 15 29 55 11 Book IV . Cor . of 5 Cor . of 11 31 Cor . 2.18 6 12 35 & 3 . 8 10 36 Book IV . 13 37 Cor . 2. of 2 14 3 38 Cor . 2. of 2 35 28 15 4 2 36 30 Cor . 1 . & 2 . Page 15

Now , since ACD is a straight line , the angle FCD will be a right angle (

Now , since ACD is a straight line , the angle FCD will be a right angle (

**Prop**. I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle . Hence , the angle FCD is equal to the angle FCE ( Ax ... Page 19

triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides , (

triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides , (

**Prop**. V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the ... Page 21

... B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle in the one , equal to two sides and the included angle in the other , each to each : hence they are equal (

... B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle in the one , equal to two sides and the included angle in the other , each to each : hence they are equal (

**Prop**. V. ) . Page 22

But if the adja- cent angles BCA , BCF , are together equal to two right angles , ACF must be a straight line (

But if the adja- cent angles BCA , BCF , are together equal to two right angles , ACF must be a straight line (

**Prop**. III . ) : from whence it fol- lows , that between the same two points , A and F , two straight lines can be drawn ...### What people are saying - Write a review

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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 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