## Elements of Geometry and Trigonometry |

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Page 17

When two triangles have these three things equal , namely , the side ED = BA , the side DF = AC , and the angle D = A , the

When two triangles have these three things equal , namely , the side ED = BA , the side DF = AC , and the angle D = A , the

**remaining**three are also respectively equal , namely , the side EF - BC , the angle E = B , and the angle F = C ... Page 24

... each to each , the

... each to each , the

**remaining**parts will also be equal , each to each , and the triangles themselves will be equal . D In the two right angled A triangles BAC , EDF , let the hypothenuse AC - DF , and the side BA = ED : then will the ... Page 33

If two opposite sides of a quadrilateral are equal and parallel , the

If two opposite sides of a quadrilateral are equal and parallel , the

**remaining**sides will also be equal and parallel , and the figure will be a parallelogram . Let ABCD be a quadrilateral , having the sides AB , CD , equal and parallel ... Page 37

If there be two sets of proportionals , having an antecedent and consequent of the first , equal to an antecedent and consequent of the second , the

If there be two sets of proportionals , having an antecedent and consequent of the first , equal to an antecedent and consequent of the second , the

**remaining**terms will be proportional . PROPOSITION V. THEOREM . Page 60

Draw the indefinite line DEF ; at any point as E , make the angle DEC equal to one of the given angles , and the angle CEH equal to the other : the

Draw the indefinite line DEF ; at any point as E , make the angle DEC equal to one of the given angles , and the angle CEH equal to the other : the

**remaining**angle HEF will be the third angle required ; be- D cause those three angles ...### 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 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