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 6
... fore the triangles ABC , DEF , are equal , the angle ABC e- qual to the angle DEF , and ACB to DFE , each to each , which the equal fides fubtend . Wherefore , & c . a Def . 4 . T PRO P. V. THE O R. HE angles above PROP 6 THE ELEMENTS.
... fore the triangles ABC , DEF , are equal , the angle ABC e- qual to the angle DEF , and ACB to DFE , each to each , which the equal fides fubtend . Wherefore , & c . a Def . 4 . T PRO P. V. THE O R. HE angles above PROP 6 THE ELEMENTS.
Seite 10
... fore , in every ifofceles triangle , the angles above the base are e- qual to one another ; and , if the fides be produced , the angles below the bafe are likewise equal to one another . PRO P. XIV . THE OR . F to any right line , and ...
... fore , in every ifofceles triangle , the angles above the base are e- qual to one another ; and , if the fides be produced , the angles below the bafe are likewise equal to one another . PRO P. XIV . THE OR . F to any right line , and ...
Seite 18
... fore the angles AGK , GKD , are each equal to GHF ; therefore equal to one another : Therefore AB is parallel to CD c . Wherefore , & c . PRO P. XXXI . PRO B. O araw a right line through a given point parallel to a given T right line ...
... fore the angles AGK , GKD , are each equal to GHF ; therefore equal to one another : Therefore AB is parallel to CD c . Wherefore , & c . PRO P. XXXI . PRO B. O araw a right line through a given point parallel to a given T right line ...
Seite 19
... fore , & c . of op F 1. Hence all the three angles of any one triangle are b Ax . I. equal to all the three angles of any other triangle , either fepa- 13 . rately or taken together . 2. If two angles of one triangle be equal to two ...
... fore , & c . of op F 1. Hence all the three angles of any one triangle are b Ax . I. equal to all the three angles of any other triangle , either fepa- 13 . rately or taken together . 2. If two angles of one triangle be equal to two ...
Seite 21
... fore , & c . COR . Hence every parallelogram is equal to a right angled parallelogram , conftitute upon the fame bafe , and between the fame parallels ; and every triangle conftitute upon the fame bafe , and betwixt the fame parallels ...
... fore , & c . COR . Hence every parallelogram is equal to a right angled parallelogram , conftitute upon the fame bafe , and between the fame parallels ; and every triangle conftitute upon the fame bafe , and betwixt the fame parallels ...
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Häufige Begriffe und Wortgruppen
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.