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 Seiten |
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Seite 36
... a 10. I. b II . I. c def . 15. 1 . d 8. r . VIII . But , when the right lines containing the angle do receive any part of the circumference , then the angle is faid to stand upon that circumference . IX . A fector of a circle is that ...
... a 10. I. b II . I. c def . 15. 1 . d 8. r . VIII . But , when the right lines containing the angle do receive any part of the circumference , then the angle is faid to stand upon that circumference . IX . A fector of a circle is that ...
Seite 37
... circumference ; therefore the right line AB is within Book III . the circle . Wherefore , & c . COR . Hence , if a ... ABCD , cutting each other in the point E , they will not mutually bifect each other ; for , if poffible , let AE be ...
... circumference ; therefore the right line AB is within Book III . the circle . Wherefore , & c . COR . Hence , if a ... ABCD , cutting each other in the point E , they will not mutually bifect each other ; for , if poffible , let AE be ...
Seite 38
... circles ABC , CDG , cut each other , they cannot have the fame center . If poffible , let E be the center of both , draw CE to the point of fection C , and EFG through any other point ; then , becaufe E is the center of the circle ABC ...
... circles ABC , CDG , cut each other , they cannot have the fame center . If poffible , let E be the center of both , draw CE to the point of fection C , and EFG through any other point ; then , becaufe E is the center of the circle ABC ...
Seite 39
... a line nearer to that paffing through the center , equal to one more remote , which cannot be . Wherefore , & c . PRO P. VIII . THE OR . .... IF a point be taken without the circle , and from it right lines be drawn , one of which ...
... a line nearer to that paffing through the center , equal to one more remote , which cannot be . Wherefore , & c . PRO P. VIII . THE OR . .... IF a point be taken without the circle , and from it right lines be drawn , one of which ...
Seite 40
... a point be affumed in 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 affumed in the circle ABC , and from it be drawn ...
... a point be affumed in 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 affumed in the circle ABC , and from it be drawn ...
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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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.