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 10,000, and Tables of Sines, Tangents, and Secants, Natural and Artificialauthor, and sold, 1776 - 264 σελίδες |
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Σελίδα xi
... ac- count of the limited fenfe in which it is taken ; for , if folid fi- gures , bounded by an equal number of equal and fimilar planes , are not equal and fimilar , but under this limitation , then prop . 15. Book V. muft not be ...
... ac- count of the limited fenfe in which it is taken ; for , if folid fi- gures , bounded by an equal number of equal and fimilar planes , are not equal and fimilar , but under this limitation , then prop . 15. Book V. muft not be ...
Σελίδα 5
... AC is equal to AB ; and because B is the center of the circle ACE ; BC c Definiti- is equal to BA , but CA is proved equal to AB , and BC to AB ; on 15 . therefore BC is equal to AC d : Therefore the three fides AB , dAxiom 1 . BC , CA ...
... AC is equal to AB ; and because B is the center of the circle ACE ; BC c Definiti- is equal to BA , but CA is proved equal to AB , and BC to AB ; on 15 . therefore BC is equal to AC d : Therefore the three fides AB , dAxiom 1 . BC , CA ...
Σελίδα 6
... equal to the lejer . Required to cut off from the greater AB a part AE , equal to the leffer C. From the point A ... AC , equal to the two fides DE , DF , each to each ; that is , AB equal to DE , and AC equal to DF , and the angle BAC ...
... equal to the lejer . Required to cut off from the greater AB a part AE , equal to the leffer C. From the point A ... AC , equal to the two fides DE , DF , each to each ; that is , AB equal to DE , and AC equal to DF , and the angle BAC ...
Σελίδα 7
... equal to the fide AC , then the angle ABC will be equal to the angle ACB . Book I. For , let a triangle DEF be likewife given , having the fides DE , DF , equal to the fides AB , AC , each to each ; and the angle BAC equal to the angle ...
... equal to the fide AC , then the angle ABC will be equal to the angle ACB . Book I. For , let a triangle DEF be likewife given , having the fides DE , DF , equal to the fides AB , AC , each to each ; and the angle BAC equal to the angle ...
Σελίδα 8
... AC , AD , are equal , the angles ADC , ACD are equal ; but the angle BDC is greater than ADC , or b Ax . 9. ACD , and much greater than BCD , but , if BD is equal to BC , the angles BCD , BDC , are equal , and likewise greater ; which ...
... AC , AD , are equal , the angles ADC , ACD are equal ; but the angle BDC is greater than ADC , or b Ax . 9. ACD , and much greater than BCD , but , if BD is equal to BC , the angles BCD , BDC , are equal , and likewise greater ; which ...
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 bafe bafe BC baſe becauſe bifected 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 reaſon fecond fegment femicircle fhall fides fimilar folid angle folid parallelopipedons fome fore fphere fquare of AC fubtending given right line greater infcribed join lefs leſs likewife magnitudes parallel parallelogram perpendicular plain paffing polygon polyhedron prifms PROP pyramid rectangle right angles right line AB right lined figure Secant Sine Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe bafe whoſe
Δημοφιλή αποσπάσματα
Σελίδα 80 - 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 72 - F, equal to them in number, be taken two and two in the fame ratio, and if their analogy be perturbate, 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 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Σελίδα x - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles.
Σελίδα 54 - Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle. It is required to place in the circle ABC a straight line equal to D.
Σελίδα 9 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 13 - 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 69 - 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...
Σελίδα 91 - 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 80 - ... 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.