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 |
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Αποτελέσματα 1 - 5 από τα 33.
Σελίδα 3
... opposite sides are equal , and its angles all right ones . XXXII . A rhombus , that which hath four equal fides , but not right angles . XXXIII . A rhomboides , whose opposite sides and angles are equal . XXXIV . All quadrilateral ...
... opposite sides are equal , and its angles all right ones . XXXII . A rhombus , that which hath four equal fides , but not right angles . XXXIII . A rhomboides , whose opposite sides and angles are equal . XXXIV . All quadrilateral ...
Σελίδα 9
... opposite side of the right line AB ; about the center C , with the distance CD , describe a circle EDG ; bisect EG in H , join CG , CH , CE ; then CH is the perpendicular required . B For 1 ! Book I. For GH , HC , are equal OF EUCLID . 9.
... opposite side of the right line AB ; about the center C , with the distance CD , describe a circle EDG ; bisect EG in H , join CG , CH , CE ; then CH is the perpendicular required . B For 1 ! Book I. For GH , HC , are equal OF EUCLID . 9.
Σελίδα 10
... opposite points , making the adjacent angles together e- qual to two right angles , these two right lines will make one conti- nued right linc . For , if to any right line AB , and point B therein , be drawn two right lines , CB , DB ...
... opposite points , making the adjacent angles together e- qual to two right angles , these two right lines will make one conti- nued right linc . For , if to any right line AB , and point B therein , be drawn two right lines , CB , DB ...
Σελίδα 11
... opposite angles are equal . Let the right lines AB , CD , mutually cut each other in the point E , the angles AEC , DEB , will be equal ; and likewise the angles CEB , AED , equal to one another . For , because the right line CE falls ...
... opposite angles are equal . Let the right lines AB , CD , mutually cut each other in the point E , the angles AEC , DEB , will be equal ; and likewise the angles CEB , AED , equal to one another . For , because the right line CE falls ...
Σελίδα 18
... opposite GKD ; there- fore the angles AGK , GKD , are each equal to GHF ; therefore equal to one another : Therefore AB is parallel to CD . Wherefore , & c . T PROP . XXXI . PROB . C 1 O araw a right line through a given point parallel ...
... opposite GKD ; there- fore the angles AGK , GKD , are each equal to GHF ; therefore equal to one another : Therefore AB is parallel to CD . Wherefore , & c . T PROP . XXXI . PROB . C 1 O araw a right line through a given point parallel ...
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.