The Geometrician: Containing Essays on Plane Geometry, and Trigonometry: with Their Application to the Solutions of a Variety of Problems ...J. Johnson, 1775 - 159 Seiten |
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Seite 22
... third Terms together ; from their Sum fubtract the Logarithm of the first Term ; and the Remainder will be the Logarithm of the fourth , or required Term . 55. Suppofe in the Rule of Three Direct we have this Stating , As 4.1 : 5 : 65 a ...
... third Terms together ; from their Sum fubtract the Logarithm of the first Term ; and the Remainder will be the Logarithm of the fourth , or required Term . 55. Suppofe in the Rule of Three Direct we have this Stating , As 4.1 : 5 : 65 a ...
Seite 25
... third Term of each refpective Stating , will give the Logarithm of the fourth , or required Term of that Stating . The Reason of this is manifeft from the Nature of Logarithms , and Chap . VIII . of the Se- cond of the Mathematical ...
... third Term of each refpective Stating , will give the Logarithm of the fourth , or required Term of that Stating . The Reason of this is manifeft from the Nature of Logarithms , and Chap . VIII . of the Se- cond of the Mathematical ...
Seite 13
... third Side . For the nearest Distance to any two Points being Pl.1.F.15 . a a Rt . Line , BA + AC must be r BC . Q. E. D. ▫ 9 . a 71. Scholium . The Epicureans , as Proclus ob- ferves , derided this Theorem , it being manifeft to the ...
... third Side . For the nearest Distance to any two Points being Pl.1.F.15 . a a Rt . Line , BA + AC must be r BC . Q. E. D. ▫ 9 . a 71. Scholium . The Epicureans , as Proclus ob- ferves , derided this Theorem , it being manifeft to the ...
Seite 16
... Third of two Rt . Angles ; or , which is equivalent , two Thirds of one Right Angle . Pl.1.F.23 . 2 78 . 568 . 86. COROLL . 8. If in any Triangle , one of its Angles is either a right or an obtufe Angle , the other two will be each of ...
... Third of two Rt . Angles ; or , which is equivalent , two Thirds of one Right Angle . Pl.1.F.23 . 2 78 . 568 . 86. COROLL . 8. If in any Triangle , one of its Angles is either a right or an obtufe Angle , the other two will be each of ...
Seite 30
... third Book . We intend hereafter to give alge- braic Demonftrations to all the Theorems of this Book . 123. Def . 1 . E BOOK III . QUAL Circles are those whofe Di- ameters are equal , or from whose Centers the Lines to the ...
... third Book . We intend hereafter to give alge- braic Demonftrations to all the Theorems of this Book . 123. Def . 1 . E BOOK III . QUAL Circles are those whofe Di- ameters are equal , or from whose Centers the Lines to the ...
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Häufige Begriffe und Wortgruppen
ABCD alfo alſo Altitude anfwering Bafe Barometer Baſe becauſe bifect Cafe Center Characteriſtick Chord Circle Circumference Cofine Compaffes confequently Conftruction contained COROLLARY decimal defcribe Degrees demonftrated Diameter Diſtance divided Divifion draw Effay equal Euclid Example faid fame Manner fame Ratio fecond Feet fhall fhew fhewn fimilar find the Height firft firſt fome ftand fubtract fuch fufficient fuppofe Geometry given Line greater Hence Hypothenufe Interfection join laft leffer lefs Logarithm Magnitudes manifeft meaſuring muſt Number obferve oppofite Sides Parallelogram Perpendicular Polygon PROBLEM Propofition Proportion quired Reaſon Rectangle Refpects reprefent right Angle right Line Scale Scholium Secant Segment Semicircle ſhall Sine Square Suppofition Tangent thefe THEOREM Thermometer theſe thoſe Triangle Trigono Trigonometry Uſe whofe
Beliebte Passagen
Seite 29 - The lines do not run in a uniform direction from the left to the right, or from the right to the left...
Seite 106 - AB, remains the same as it was : Nor is it part of the length of the line AB ; for, if AB be removed from the line KB, the point B, which is the extremity of the line KB, does...
Seite 120 - If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle. Let...
Seite 15 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Seite 43 - ... magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first A is said to have to the last D the ratio compounded of the ratio of A to B, and of the ratio of B to C, and of the ratio of C to D; or, the ratio of A to D is said to be compounded of the ratios of A to B, B to C, and C to D. And if...
Seite 106 - It is necessary to consider a solid, that is, a magnitude which has length, breadth, and thickness, in order to understand aright the definitions of a point, line and superficies ; for these all arise from a solid, and exist in it ; The boundary, or boundaries which contain a solid, are called superficies, or the boundary which is common to two solids which are contiguous, or which divides one solid into two contiguous parts, is called a superficies...
Seite 43 - When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second.
Seite 64 - ... is supposed to be divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters ° ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10° 18
Seite 18 - If two triangles have two sides of the one equal to two sides of the...
Seite 106 - KBCL which is contiguous to it, this boundary BC is called a line, and has no breadth : For if it have any, this...