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 sider |
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Resultat 1-5 av 56
Side iii
... Tangents , and Secants , Natural and Artificial . BY GEORGE DOUGLAS , Teacher of Mathematics in the Academy at Ayr . E DIN BURG H Printed for the AUTHOR , and fold by C. ELLIOT , Edinburgh , and RICHARDSON and URQUHART , London . M ...
... Tangents , and Secants , Natural and Artificial . BY GEORGE DOUGLAS , Teacher of Mathematics in the Academy at Ayr . E DIN BURG H Printed for the AUTHOR , and fold by C. ELLIOT , Edinburgh , and RICHARDSON and URQUHART , London . M ...
Side ix
... Tangents , Secants , and verfed Sines , both natural and artificial ; and how to change Briggs's Logarithms to the Hyper- bolic , and vice verfa , with examples of the above . To which are annexed TABLES of the Logarithms of Numbers ...
... Tangents , Secants , and verfed Sines , both natural and artificial ; and how to change Briggs's Logarithms to the Hyper- bolic , and vice verfa , with examples of the above . To which are annexed TABLES of the Logarithms of Numbers ...
Side 44
... tangent required . For , because E is the center of both circles , the right lines AE , EB , are equal to FE , ED , and the angle E common ; therefore the triangle ABE is equal to FDE c ; and the angle EBA to EDF ; but EDF is a right ...
... tangent required . For , because E is the center of both circles , the right lines AE , EB , are equal to FE , ED , and the angle E common ; therefore the triangle ABE is equal to FDE c ; and the angle EBA to EDF ; but EDF is a right ...
Side 45
... tangent ; and if , from the point of con- tact , a right line be drawn , 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 ...
... tangent ; and if , from the point of con- tact , a right line be drawn , 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 ...
Side 50
... tangent are equal to the angles in the alternate feg- ments of the circle . Let the right line EF touch the circle ABCD in the point B ; from any point D , in the circle , draw the right line DB ; then the angle DBF is equal to the ...
... tangent are equal to the angles in the alternate feg- ments of the circle . Let the right line EF touch the circle ABCD in the point B ; from any point D , in the circle , draw the right line DB ; then the angle DBF is equal to the ...
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Vanlige uttrykk og setninger
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Populære avsnitt
Side 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.
Side 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.
Side 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.