Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and ExplanatoryJohnson, 1803 - 279 páginas |
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Página 7
... also equal to AB ( Def . 13. ) But things which are equal to the fame thing are equal to each other ( 4x . 1 ) ; therefore AC 18 equal to CB . And , fince AC , CB are equal to each other , as well as to AB , the triangle , ABC is ...
... also equal to AB ( Def . 13. ) But things which are equal to the fame thing are equal to each other ( 4x . 1 ) ; therefore AC 18 equal to CB . And , fince AC , CB are equal to each other , as well as to AB , the triangle , ABC is ...
Página 8
... equal to a given finite right line . E D Let A be the given point , and BC the given right line ; it is required to ... also be equal to BC ( Ax . 1. ) A right line AG , has , therefore , been drawn from the point A , equal to the right ...
... equal to a given finite right line . E D Let A be the given point , and BC the given right line ; it is required to ... also be equal to BC ( Ax . 1. ) A right line AG , has , therefore , been drawn from the point A , equal to the right ...
Página 11
... equal to each other . D C Let ABC be an isofceles triangle , having the fide ca equal to the fide CB ; then will the ... also be equal to the remaining part BE ( Ax . 3. ) Hence , the two fides DA , DB , of the triangle DAB , being equal ...
... equal to each other . D C Let ABC be an isofceles triangle , having the fide ca equal to the fide CB ; then will the ... also be equal to the remaining part BE ( Ax . 3. ) Hence , the two fides DA , DB , of the triangle DAB , being equal ...
Página 12
... equal to the remaining angle CBA ( Ax . 3. ) Q. E.D. COROLLARY . Every equilateral triangle is also equi- angular . PROP . VI . THEOREM . If two angles of a triangle be equal to each other , the fides which are oppofite to them will also be ...
... equal to the remaining angle CBA ( Ax . 3. ) Q. E.D. COROLLARY . Every equilateral triangle is also equi- angular . PROP . VI . THEOREM . If two angles of a triangle be equal to each other , the fides which are oppofite to them will also be ...
Página 13
... equal to the three fides of another , each to each , the angles which are oppofite to the equal fides will alfo be ... also , be be equal to the angle GAB , and the angle BOOK THE FIRST . 18.
... equal to the three fides of another , each to each , the angles which are oppofite to the equal fides will alfo be ... also , be be equal to the angle GAB , and the angle BOOK THE FIRST . 18.
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Otras ediciones - Ver todas
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página xii - The radius of a circle is a right line drawn from the centre to the circumference.
Página 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.
Página 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.