## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and Illustrations |

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Side 28

... it will make the alternate angles equal , the exterior angle equal to the interior opposite one , and the two interior angles on

... it will make the alternate angles equal , the exterior angle equal to the interior opposite one , and the two interior angles on

**the same side together equal to two right angles . Let the straight line**EFG fall upon the parallels AB ...### Hva folk mener - Skriv en omtale

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Elements of geometry, geometrical analysis, and plane trigonometry Sir John Leslie Uten tilgangsbegrensning - 1811 |

Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1809 |

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alternate ANALYSIS base bisect Book centre chord circle circumference common COMPOSITION consequently construction contained corresponding describe diameter difference distance divided double draw drawn equal equivalent evidently extended exterior angle extreme figure four given given circle given in position given point given ratio given space greater half hence inflected inscribed intercepted intersection join less let fall likewise mean measure meet opposite parallel perpendicular polygon portion PROB produce PROP proportional proposition quantities radius ratio reason rectangle remaining rhomboid right angles segments semicircle sides similar sine square square of AC straight line tangent THEOR third tion triangle ABC twice vertical angle whence wherefore whole

### Populære avsnitt

Side 28 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Side 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.

Side 92 - THE angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same

Side 458 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Side 99 - ... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.

Side 155 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.

Side 408 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Side 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...

Side 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 60 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.