Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and Explanatory |
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Page 11
... CBD , and the angle c is common , the fide AE will alfo be equal to the fide BD , the angle CAE to the angle CBD , and the angle D to the angle E ( Prop . 4. ) And fince the whole CD is equal to the whole CE ( by Conft . ) , and the ...
... CBD , and the angle c is common , the fide AE will alfo be equal to the fide BD , the angle CAE to the angle CBD , and the angle D to the angle E ( Prop . 4. ) And fince the whole CD is equal to the whole CE ( by Conft . ) , and the ...
Page 16
... angle DAF will be equal to the angle FAE ; and con- fequently the angle BAC is bifected by the right line af , as ... CBD ( by Conft . ) But when two fides and the included angle of one tri- angle , are equal to two fides and the ...
... angle DAF will be equal to the angle FAE ; and con- fequently the angle BAC is bifected by the right line af , as ... CBD ( by Conft . ) But when two fides and the included angle of one tri- angle , are equal to two fides and the ...
Page 17
... angle are equal to each other . C Let ABC be an isofceles triangle , having the fide ca equal to the fide CB ; then ... CBD , and the angle c is common , the fide AE will also be equal to the fide BD , the angle CAE to the angle CBD ...
... angle are equal to each other . C Let ABC be an isofceles triangle , having the fide ca equal to the fide CB ; then ... CBD , and the angle c is common , the fide AE will also be equal to the fide BD , the angle CAE to the angle CBD ...
Page x
... angle DAF will be equal to the angle FAE ; and con- fequently the angle BAC is bifected by the right line AF , as ... CBD ( by Conft . ) But when two fides and the included angle of one tri- angle , are equal to two fides and the ...
... angle DAF will be equal to the angle FAE ; and con- fequently the angle BAC is bifected by the right line AF , as ... CBD ( by Conft . ) But when two fides and the included angle of one tri- angle , are equal to two fides and the ...
Page xii
... CBD is one continued right line , as was to be fhewn . PRO P. XV . THEOREM . If two right lines interfect each other , the oppofite angles will be equal . Let the two right lines AB , CD interfect each other in the point E ; then will the ...
... CBD is one continued right line , as was to be fhewn . PRO P. XV . THEOREM . If two right lines interfect each other , the oppofite angles will be equal . Let the two right lines AB , CD interfect each other in the point E ; then will the ...
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Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle No preview available - 2016 |
Common terms and phrases
ABCD abfurd alfo equal alſo be equal alternate angle altitude angle ABC angle ACB angle AGH angle BAC angle CAB angle CBD angle DEF angle EGB bafe baſe becauſe bifect centre circle ABC circumference Conft COROLL demonftrated diagonal diſtance draw equal and parallel equal to BC equiangular equimultiples EUCLID fame manner fame multiple fame parallels fame ratio fection fegment fhewn fide AB fide BC fince the angles folid fome fquares of AC given right line interfect join the points lefs leſs Let ABC Let the right magnitudes muſt oppofite angle outward angle parallel right lines parallelogram parallelogram AC perpendicular polygon Prop propofition Q.E.D. PROP rectangle of AC remaining angle right angles right lines AB ſame SCHOLIUM ſquare ſtand taken THEOREM theſe thoſe three fides triangle ABC whence
Popular passages
Page 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.
Page 31 - THE Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, is Equal to the Angle in the Alternate Segment.
Page xii - 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page xii - The radius of a circle is a right line drawn from the centre to the circumference.
Page 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.
Page 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.