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 Artificial |
From inside the book
Results 1-5 of 22
Page 37
... paffing through the centre , cutting the right line AB , not paffing through the centre , into two equal parts , it will cut it at right angles ; and if the angles AFE , EFB , be right angles , AF will be equal to FB . c 8. I. I. For ...
... paffing through the centre , cutting the right line AB , not paffing through the centre , into two equal parts , it will cut it at right angles ; and if the angles AFE , EFB , be right angles , AF will be equal to FB . c 8. I. I. For ...
Page 39
... paffing through the center ; and the line nearer to that , paffing through the center , is greater than that more re- mote ; of thofe falling upon the convex part of the circumference , that which lies betwixt the point and the diameter ...
... paffing through the center ; and the line nearer to that , paffing through the center , is greater than that more re- mote ; of thofe falling upon the convex part of the circumference , that which lies betwixt the point and the diameter ...
Page 40
... paffing through the center , equal to one more remote . Wherefore , & c . i 4. z . PRO P. IX . THE OR . TF 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 ...
... paffing through the center , equal to one more remote . Wherefore , & c . i 4. z . PRO P. IX . THE OR . TF 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 ...
Page 45
... paffing through the circle , at right angles to the tangent , the center of the circle will be in that line . Let ABC be a circle , and DE a right line touching it in the point C ; and if , from the center F , there be drawn a right ...
... paffing through the circle , at right angles to the tangent , the center of the circle will be in that line . Let ABC be a circle , and DE a right line touching it in the point C ; and if , from the center F , there be drawn a right ...
Page 52
... paffing through the center , cut BD , not paffing through the center , at right angles , in the point E , find the center F , and join FD ; for , because BE is equal to ED 6 , and the angle DEF is a right one , the fquares of DE , EF ...
... paffing through the center , cut BD , not paffing through the center , at right angles , in the point E , find the center F , and join FD ; for , because BE is equal to ED 6 , and the angle DEF is a right one , the fquares of DE , EF ...
Other editions - View all
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid No preview available - 2015 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.