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 10
... fide CA with the fide FD . Then , because CA coincides with FD , and the angle c is equal to the angle ( by Hyp . ) , the fide CB will also coincide with the fide FE . 8 And , fince CA is equal to FD , and CB to FE ( by Hyp . ) , the ...
... fide CA with the fide FD . Then , because CA coincides with FD , and the angle c is equal to the angle ( by Hyp . ) , the fide CB will also coincide with the fide FE . 8 And , fince CA is equal to FD , and CB to FE ( by Hyp . ) , the ...
Σελίδα 11
... fide ca equal to the fide CB ; then will the angle CAB be equal to the angle CBA . # For , in CA and CB produced , take any two equal parts CD , CE ( Prop . 3. ) , and join the points AE , BD : Then , because the two fides CA , CE of ...
... fide ca equal to the fide CB ; then will the angle CAB be equal to the angle CBA . # For , in CA and CB produced , take any two equal parts CD , CE ( Prop . 3. ) , and join the points AE , BD : Then , because the two fides CA , CE of ...
Σελίδα 12
... fide CA be equal to the fide CB . For if CA be not equal to CB , one of them must be greater than the other ; let CA be the greater , and make AD equal to BC ( Prop . 3. ) and join BD . Then , because the two fides AD , AB , of the ...
... fide CA be equal to the fide CB . For if CA be not equal to CB , one of them must be greater than the other ; let CA be the greater , and make AD equal to BC ( Prop . 3. ) and join BD . Then , because the two fides AD , AB , of the ...
Σελίδα 13
... fide DE , AC to DF , and BC to EF ; then will the angle ACB be equal to the angle DFE , BAC to EDF , and ABC to DEF ... fide AC is equal to the fide DF , or AC ( by Hyp . ) , the angle ACG will be equal to the angle ACC ( Prop . 5. ) And ...
... fide DE , AC to DF , and BC to EF ; then will the angle ACB be equal to the angle DFE , BAC to EDF , and ABC to DEF ... fide AC is equal to the fide DF , or AC ( by Hyp . ) , the angle ACG will be equal to the angle ACC ( Prop . 5. ) And ...
Σελίδα 16
... fide Dr , therefore , being equal to the fide FE , the angle DAF will be equal to the angle FAE ; and con- fequently the angle BAC is bifected by the right line af , as was to be done . PROP . X. PROBLEM . To bifect a given finite right ...
... fide Dr , therefore , being equal to the fide FE , the angle DAF will be equal to the angle FAE ; and con- fequently the angle BAC is bifected by the right line af , as was to be done . PROP . X. PROBLEM . To bifect a given finite right ...
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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.