Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and Explanatory
Johnson, 1803 - 279 σελίδες
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Elements of Geometry: Containing the Principal Propositions in the First Six ...
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ABCD alſo be equal alſo equal alternate angle altitude angle ABC angle ACB angle BAC angle CAB angle CBD baſe becauſe biſect BOOK centre chord circle circle ABC circumference common Conft conſequently contained COROLL demonſtration deſcribe diagonal diameter difference diſtance divide double draw drawn equiangular equimultiples EUCLID fall fame baſe fide figure fince firſt four given point given right line greater half interſects leſs Let ABC line AC magnitudes meet muſt oppoſite angle outward angle parallel parallelogram perpendicular plane polygon PROBLEM produced Prop proportional propoſition rectangle remaining angle right angles ſame ſame manner ſame multiple ſection ſegment ſhall ſhewn ſide ſide bc ſince ſome ſquare ſtand ſum taken THEOREM theſe thing third triangle triangle ABC whence whole whoſe
Σελίδα 63 - AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length to become greater than AB.
Σελίδα 17 - To find the centre of a given circle. Let ABC be the given circle ; it is required to find its centre. Draw within it any straight line AB, and bisect (I.
Σελίδα xxiii - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Σελίδα 63 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Σελίδα 24 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw* the straight line GAH touching the circle in the a 17. 3. point A, and at the point A, in the straight line AH, makeb b 23.
Σελίδα i - ELEMENTS of GEOMETRY, containing the principal Propositions in the first Six and the Eleventh and Twelfth Books of Euclid, with Critical Notes ; and an Appendix, containing various particulars relating to the higher part* of the Sciences.
Σελίδα 17 - The radius of a circle is a right line drawn from the centre to the circumference.
Σελίδα 30 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Σελίδα 7 - Beciprocally, when these properties exist for 'two right lines and a common secant, the two lines are parallel.* — Through a given point, to draw a right line parallel to a given right line, or cutting it at a given angle, — Equality of angles having their sides parallel and their openings placed in the same direction.