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 σελίδες |
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Σελίδα 114
... polygons ; and if the angles , as well as fides , are all equal , they are called regular polygons . 9. Polygons of five fides , are called pentagons ; those of fix fides hexagons ; those of seven heptagons ; and fo on . 1 PROP . I ...
... polygons ; and if the angles , as well as fides , are all equal , they are called regular polygons . 9. Polygons of five fides , are called pentagons ; those of fix fides hexagons ; those of seven heptagons ; and fo on . 1 PROP . I ...
Σελίδα 133
... polygon can be described , by any known method , purely geometrical . It may also be observed that fome of these figures , as well as feveral others , in the former part of the work , may often be described in a much easier way , for ...
... polygon can be described , by any known method , purely geometrical . It may also be observed that fome of these figures , as well as feveral others , in the former part of the work , may often be described in a much easier way , for ...
Σελίδα 180
... and the fquare DN is double the triangle DME , the triangle ABC will be to the triangle DEF as the fquare AL is to the fquare DN ( V. 13 and 15. ) Q. E.D. PROP . XVII . THEOREM . Similar polygons are to PROP . 180 ELEMENTS OF GEOMETRY .
... and the fquare DN is double the triangle DME , the triangle ABC will be to the triangle DEF as the fquare AL is to the fquare DN ( V. 13 and 15. ) Q. E.D. PROP . XVII . THEOREM . Similar polygons are to PROP . 180 ELEMENTS OF GEOMETRY .
Σελίδα 181
... polygons are to each other as the fquares of their homologous fides . E A B Let ABCDE , FGHIK be fimilar polygons , of which AB , FG are homologous fides ; then will the polygon ABCDES be to the polygon FGHIK as the fquare of AB is to ...
... polygons are to each other as the fquares of their homologous fides . E A B Let ABCDE , FGHIK be fimilar polygons , of which AB , FG are homologous fides ; then will the polygon ABCDES be to the polygon FGHIK as the fquare of AB is to ...
Σελίδα 182
... polygon ABCDE will be to the polygon FGHIK as the triangle EAB is to the triangle KFG . But the triangle EAB is to the triangle KFG as the fquare of AB is to the square of FG ( VI . 16. ) ; whence the polygon ABCDE is also to the ...
... polygon ABCDE will be to the polygon FGHIK as the triangle EAB is to the triangle KFG . But the triangle EAB is to the triangle KFG as the fquare of AB is to the square of FG ( VI . 16. ) ; whence the polygon ABCDE is also to the ...
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Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
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 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.
Σελίδα 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.
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 xii - 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.