The Geometrician: Containing Essays on Plane Geometry, and Trigonometry: with Their Application to the Solutions of a Variety of Problems ...J. Johnson, 1775 - 159 sider |
Inni boken
Resultat 1-5 av 8
Side 2
... Extremes of a Line are called Points . * 4 . 9. A right Line , or ftraight Line , is that which lies evenly between its Points ; or which is the short- eft Distance from its extreme Points . And a Line , which lies unevenly between its ...
... Extremes of a Line are called Points . * 4 . 9. A right Line , or ftraight Line , is that which lies evenly between its Points ; or which is the short- eft Distance from its extreme Points . And a Line , which lies unevenly between its ...
Side 54
... Extremes is equal to the Rectangle under the Means , viz . a x d = bxc . And if the Rectangle contained by the Extremes be the Rectangle contained by the Means , thefe four Quantities are proportional ; that is , if a x dbx c , then it ...
... Extremes is equal to the Rectangle under the Means , viz . a x d = bxc . And if the Rectangle contained by the Extremes be the Rectangle contained by the Means , thefe four Quantities are proportional ; that is , if a x dbx c , then it ...
Side 57
... Extremes being the Rectangle of the Means , a x d = bx c ; or , which is the fame , bx c = ax d , · .. b : a * :: d : c . xd , Q. E. D. 199. THEOREM 12. If four Quantities be propor- tional , they will also be proportional when taken ...
... Extremes being the Rectangle of the Means , a x d = bx c ; or , which is the fame , bx c = ax d , · .. b : a * :: d : c . xd , Q. E. D. 199. THEOREM 12. If four Quantities be propor- tional , they will also be proportional when taken ...
Side 58
... Extremes , a - b x dad bd , and the Product of the bd ; but ad be by Art . 193 , confe- bd ; or , which is the fame , a- Means bx c d = bc quently ad bd = bc - = b x c -d ; ··· a b x d --- b : b :: c d d . QE . D. * Algebraically thus ...
... Extremes , a - b x dad bd , and the Product of the bd ; but ad be by Art . 193 , confe- bd ; or , which is the fame , a- Means bx c d = bc quently ad bd = bc - = b x c -d ; ··· a b x d --- b : b :: c d d . QE . D. * Algebraically thus ...
Side 59
... Extremes is equal to * I 2 the Analytically thus . The Product of the Extremes a + b x c - d = ac + bc ad bd ; and the Product of the Means - a_b x c + d = ac bc + ad bd . comm But it is known that ad = + be — ad in one Equa- be by the ...
... Extremes is equal to * I 2 the Analytically thus . The Product of the Extremes a + b x c - d = ac + bc ad bd ; and the Product of the Means - a_b x c + d = ac bc + ad bd . comm But it is known that ad = + be — ad in one Equa- be by the ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 29 - The lines do not run in a uniform direction from the left to the right, or from the right to the left...
Side 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...
Side 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...
Side 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.
Side 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...
Side 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...
Side 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.
Side 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
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 106 - KBCL which is contiguous to it, this boundary BC is called a line, and has no breadth : For if it have any, this...