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 28
... BC , and the angle DAC to the angle ACB ( Prop . 4. ) Since , therefore ... side BC ( Def , 22. ) , and the right line AC interfects them , the angle ... angle angle 38 ELEMENTS OF GEOMETRY ,
... BC , and the angle DAC to the angle ACB ( Prop . 4. ) Since , therefore ... side BC ( Def , 22. ) , and the right line AC interfects them , the angle ... angle angle 38 ELEMENTS OF GEOMETRY ,
Σελίδα 30
... BC , and the angle DAC to the angle AÇв ( Prop.4 . ) Since , therefore , the ... side BC ( Def , 22. ) , and the right line AC interfects them , the angle ... angle angle 38 ELEMENTS OF GEOMÉTRY ,
... BC , and the angle DAC to the angle AÇв ( Prop.4 . ) Since , therefore , the ... side BC ( Def , 22. ) , and the right line AC interfects them , the angle ... angle angle 38 ELEMENTS OF GEOMÉTRY ,
Σελίδα 50
... BC , equal to FG ( I. 3. ) ; and join KL . Then , because BK is equal to FE , BL to FG , and the angle KBL to the ... side EF . For if AB be not greater than EF , it must be either equal to it , or lefs ; but it cannot be equal to it ...
... BC , equal to FG ( I. 3. ) ; and join KL . Then , because BK is equal to FE , BL to FG , and the angle KBL to the ... side EF . For if AB be not greater than EF , it must be either equal to it , or lefs ; but it cannot be equal to it ...
Σελίδα 53
... BC , the angle CAB will be equal to the angle ACB ( I. 5. ) And because the right line GH is parallel to the right ... side HK ( I. 6. ) E 3 But But the fide AH is equal to the fide EK BOOK THE SECOND . 53.
... BC , the angle CAB will be equal to the angle ACB ( I. 5. ) And because the right line GH is parallel to the right ... side HK ( I. 6. ) E 3 But But the fide AH is equal to the fide EK BOOK THE SECOND . 53.
Σελίδα 66
... BC ( II . 14. ) ; whence the fquare of AC is greater than the fsquares of AB ... side , by twice the rectangle of the base and the distance of the ... BC , by twice the rectangle of AB , BD . For , fince AB , or AB produced , is divided ...
... BC ( II . 14. ) ; whence the fquare of AC is greater than the fsquares of AB ... side , by twice the rectangle of the base and the distance of the ... BC , by twice the rectangle of AB , BD . For , fince AB , or AB produced , is divided ...
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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.