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 xii
... outward angle will be greater than either of the inward opposite angles . R B Let ABC be a triangle , having the fide AB produced to D ; then will the outward angle ... angle CBD is greater than the angle EBF But 22 ELEMENTS OF GEOMETRY .
... outward angle will be greater than either of the inward opposite angles . R B Let ABC be a triangle , having the fide AB produced to D ; then will the outward angle ... angle CBD is greater than the angle EBF But 22 ELEMENTS OF GEOMETRY .
Page xii
... outward angle ADC is greater than the inward oppofite angle DBC ( Prop . 16. ) But the angle ACD is equal to the angle ADC , because AC is equal to AD ; confequently the angle ACD is , alfo ... angle GAB , and the angle BOOK THE FIRST . 23.
... outward angle ADC is greater than the inward oppofite angle DBC ( Prop . 16. ) But the angle ACD is equal to the angle ADC , because AC is equal to AD ; confequently the angle ACD is , alfo ... angle GAB , and the angle BOOK THE FIRST . 23.
Page 22
... outward angle will be greater than either of the inward oppofite angles . 4 B Let ABC be a triangle , having the fide AB produced to D ; then will the outward angle ... angle CBD is greater than the angle EBF But 22 ELEMENTS OF GEOMETRY .
... outward angle will be greater than either of the inward oppofite angles . 4 B Let ABC be a triangle , having the fide AB produced to D ; then will the outward angle ... angle CBD is greater than the angle EBF But 22 ELEMENTS OF GEOMETRY .
Page 23
... angle CBD is greater than the angle EBF ; com fequently it is also greater than the angle ACE . And , if CB be ... outward angle ADC is greater than the inward oppofite angle DBC ( Prop . 16. ) But the angle ACD is equal to the angle ADC ...
... angle CBD is greater than the angle EBF ; com fequently it is also greater than the angle ACE . And , if CB be ... outward angle ADC is greater than the inward oppofite angle DBC ( Prop . 16. ) But the angle ACD is equal to the angle ADC ...
Page 29
... angle FDE , the fide BC will alfo be equal to the fide EF , and the two triangles will be equal in all respects ... outward angle AES is greater than the inward oppofite angle EFD ( Prop , 16 . ) - But But the angles , AEF , EFD , are ...
... angle FDE , the fide BC will alfo be equal to the fide EF , and the two triangles will be equal in all respects ... outward angle AES is greater than the inward oppofite angle EFD ( Prop , 16 . ) - But But the angles , AEF , EFD , are ...
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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.