The Elements of Euclid,: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10000, and Tables of Sines, Tangents, and Secants, Both Natural and ArtificialJ. Murray, no. 32. Fleetstreet; and C. Elliot, Parliament-square, Edinburgh., 1776 - 264 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 36
... circles are those which include equal angles or whereof the angles in them are equal . PROP . I. PR B. O find the centre of a circle . 1 Required to find the centre of the given circle ABC . Draw in it the line AB , which bisect in Da ...
... circles are those which include equal angles or whereof the angles in them are equal . PROP . I. PR B. O find the centre of a circle . 1 Required to find the centre of the given circle ABC . Draw in it the line AB , which bisect in Da ...
Σελίδα 37
... ABC be the given circle , CD the line passing through the centre , cutting the right line AB , not passing through the centre , into two equal parts , it will cut it at right angles ; and if the angles AFE , EFB , be right angles , AF ...
... ABC be the given circle , CD the line passing through the centre , cutting the right line AB , not passing through the centre , into two equal parts , it will cut it at right angles ; and if the angles AFE , EFB , be right angles , AF ...
Σελίδα 38
... circles ABC , CDG , cut each other , they cannot have the fame center . } a If poffible , let E be the center of both , draw CE to the point of festion C , and EFG through any other point ; then , because E is the center of the circle ABC ...
... circles ABC , CDG , cut each other , they cannot have the fame center . } a If poffible , let E be the center of both , draw CE to the point of festion C , and EFG through any other point ; then , because E is the center of the circle ABC ...
Σελίδα 39
... circle , EA is equal to EB ; add EF to both ; then AF is equal to BE , EF ; but BE , EF , are greater than BF2 ... ABC ; draw DA , DE , DF , DC , to the concave part of the circumference ; of thesc lines DA , which passes through ...
... circle , EA is equal to EB ; add EF to both ; then AF is equal to BE , EF ; but BE , EF , are greater than BF2 ... ABC ; draw DA , DE , DF , DC , to the concave part of the circumference ; of thesc lines DA , which passes through ...
Σελίδα 40
... circle , and from a circle , and from it be drawn more than two right lines to the circumference equal to one another , that point is the center of the circle . Let the point D be assumed in the circle ABC , and from it be drawn , to the ...
... circle , and from a circle , and from it be drawn more than two right lines to the circumference equal to one another , that point is the center of the circle . Let the point D be assumed in the circle ABC , and from it be drawn , to the ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCM angle ABC angle BAC arch baſe BC becauſe biſect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder DEFH deſcribe diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reaſon fides fimilar firſt folid angle fore fubtend given right line greater inſcribed join leſs Let ABC likewife magnitudes oppoſite parallel parallelogram perpendicular plain angles polygon priſm PROB PROP pyramid rectangle right angles right lined figure ſame Secant ſecond ſegment ſhall ſide Sine ſolid ſome ſphere ſquare ſquare of AC Tang tangent THEOR theſe triangle ABC triplicate ratio verſed Wherefore whoſe baſe
Δημοφιλή αποσπάσματα
Σελίδα 93 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the...
Σελίδα 78 - ... viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
Σελίδα 88 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Σελίδα 19 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Σελίδα 75 - Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in DE equal...
Σελίδα 88 - ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2.
Σελίδα 99 - BGC: for the same reason, whatever multiple the circumference EN is of the circumference EF, the same multiple is the angle EHN of the angle EHF: and if the circumference BL be equal to the circumference EN, the angle BGL is also equal to the angle EHN ; (in.
Σελίδα 106 - ... but BD, BE, which are in that plane, do each of them meet AB ; therefore each of the angles ABD, ABE is a right angle ; for the same reason, each of the angles CDB, CDE is a right angle: and because AB is equal to DE, and BD...
Σελίδα 73 - RATIOS that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F ; A is to B, as E to F.