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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Σελίδα viii
... whole is fhorter than that presently ufed . In the 16th , " the angle of a " femicircle " is omitted , because it follows more naturally as a corollary . The 18th and 19th are joined in one , for the rea- fons already given . I have put ...
... whole is fhorter than that presently ufed . In the 16th , " the angle of a " femicircle " is omitted , because it follows more naturally as a corollary . The 18th and 19th are joined in one , for the rea- fons already given . I have put ...
Σελίδα ix
... both natural and artificial , which will work to the fame exactnefs , of any extant , even to fecond and third ininutes , or farther , if thought neceflary , Upon Upon the whole , although the above alterations are intended PREFACE . ix.
... both natural and artificial , which will work to the fame exactnefs , of any extant , even to fecond and third ininutes , or farther , if thought neceflary , Upon Upon the whole , although the above alterations are intended PREFACE . ix.
Σελίδα x
... whole , although the above alterations are intended to render the elements eafier and fooner acquired , yet are not intended to indulge the indolence of either mafter or ftu . dent . The Elements of Geometry being of fuch extensive ufe ...
... whole , although the above alterations are intended to render the elements eafier and fooner acquired , yet are not intended to indulge the indolence of either mafter or ftu . dent . The Elements of Geometry being of fuch extensive ufe ...
Σελίδα 3
... from equal things equal things be taken , the remainders will be equal . IV1 If to unequal things equal things are added , the whole will be unequal , V. I £ Book I. BOOK I V. I from unequal things equal parts are OF EUCLID . lem.
... from equal things equal things be taken , the remainders will be equal . IV1 If to unequal things equal things are added , the whole will be unequal , V. I £ Book I. BOOK I V. I from unequal things equal parts are OF EUCLID . lem.
Σελίδα 4
... whole is greater than its part . X. Two right lines do not bound a figure . XI . All right angles are equal to one another . XII . If a right line fall upon two right lines , making the inward angles on the fame fide lefs than two right ...
... whole is greater than its part . X. Two right lines do not bound a figure . XI . All right angles are equal to one another . XII . If a right line fall upon two right lines , making the inward angles on the fame fide lefs than two right ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCM angle ABC angle BAC arch bafe baſe becauſe bifect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder defcribe DEFH diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reafon fecond fegment femicircle fides fimilar folid angle fome fore fquare of AC fubtending given right line greater infcribed join lefs leſs Let ABC magnitudes oppofite parallel parallelogram perpendicular plain angles plain paffing polygon prifms Prop pyramid rectangle right angles right line AB right lined figure Secant Sine ſphere ſquare Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe ΙΟ
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.