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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Αποτελέσματα 1 - 5 από τα 65.
Σελίδα xii
... ABC ; then , if the folid EABC is not equal to the folid FABC , let it be equal to fome folid as GA BC , either greater or lefs than EABC , which cannot be ; for the one would contain the other ; and if the folid angle ... angles , e- qual ...
... ABC ; then , if the folid EABC is not equal to the folid FABC , let it be equal to fome folid as GA BC , either greater or lefs than EABC , which cannot be ; for the one would contain the other ; and if the folid angle ... angles , e- qual ...
Σελίδα 6
... angles of the other , each to each , which the equal fides fubtend Let the two triangles be ABC , DEF , having the two fides AB , AC , equal to the two fides DE , DF , each to each ; that is , AB equal to DE , and AC equal to DF , and the ...
... angles of the other , each to each , which the equal fides fubtend Let the two triangles be ABC , DEF , having the two fides AB , AC , equal to the two fides DE , DF , each to each ; that is , AB equal to DE , and AC equal to DF , and the ...
Σελίδα 7
... angles above the base of every ifofceles triangle are e- qual to one another . Let the triangle ABC be the ifofceles triangle , having the fide AB equal to the fide AC , then the angle ABC will be equal to the angle ACB . Book I. For , let ...
... angles above the base of every ifofceles triangle are e- qual to one another . Let the triangle ABC be the ifofceles triangle , having the fide AB equal to the fide AC , then the angle ABC will be equal to the angle ACB . Book I. For , let ...
Σελίδα 8
... ABC , DEF , having the two fides AB , AC , equal to the two fides DE , DF , each to each ; and the bafes BC , EF ... angle BAC is equal to the angle EDF . Wherefore , & c . To cut a PRO P. IX . PRO B. O cut a given right lined angle into ...
... ABC , DEF , having the two fides AB , AC , equal to the two fides DE , DF , each to each ; and the bafes BC , EF ... angle BAC is equal to the angle EDF . Wherefore , & c . To cut a PRO P. IX . PRO B. O cut a given right lined angle into ...
Σελίδα 9
... triangle ABC ; bi- fect the angle ACB by the right line CD ; then is the right a line AB bifected in D. For , because AC is equal to CB , and CD common , and the angles ACD , BCD , equal , the bafes AD , BD , are equal b : b Therefore ...
... triangle ABC ; bi- fect the angle ACB by the right line CD ; then is the right a line AB bifected in D. For , because AC is equal to CB , and CD common , and the angles ACD , BCD , equal , the bafes AD , BD , are equal b : b Therefore ...
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.