Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 sider |
Inni boken
Resultat 1-5 av 32
Side 152
... expressed , by inserting points in pairs between the terms . Thus A : B denotes the ratio of A to B , and the compound symbols A : B :: C : D , signify that the ratio of A to B is the same as that of C to D , or that A is to B as C to D ...
... expressed , by inserting points in pairs between the terms . Thus A : B denotes the ratio of A to B , and the compound symbols A : B :: C : D , signify that the ratio of A to B is the same as that of C to D , or that A is to B as C to D ...
Side 163
... the difference of the homologous terms , and may , therefore , be more generally expressed thus : A : B :: ACE ÷ G : B ÷ DF ÷ H . Cor . 2. Hence , if A : B :: C : D , and A : E :: C : F ; then A : C :: BE : DF . For , BOOK V. 163.
... the difference of the homologous terms , and may , therefore , be more generally expressed thus : A : B :: ACE ÷ G : B ÷ DF ÷ H . Cor . 2. Hence , if A : B :: C : D , and A : E :: C : F ; then A : C :: BE : DF . For , BOOK V. 163.
Side 172
... expression thus obtained must constantly approach to the ratio of A : B , since they suppose only the omission of the remainder of the last division , and which is perpetu- ally diminishing . PROP . XXVII . THEOR . A straight line is ...
... expression thus obtained must constantly approach to the ratio of A : B , since they suppose only the omission of the remainder of the last division , and which is perpetu- ally diminishing . PROP . XXVII . THEOR . A straight line is ...
Side 177
... expressed numerically , and that to any required degree of precision . AD being divided into equal parts ( I. 40. ) , these parts , continued towards B , will , together with a subsidiary portion , compose the whole of M AB . Let this ...
... expressed numerically , and that to any required degree of precision . AD being divided into equal parts ( I. 40. ) , these parts , continued towards B , will , together with a subsidiary portion , compose the whole of M AB . Let this ...
Side 226
... expressed by A , its sides by a , b , and c , and the semiperimeter by s ; then s ( sa ) : A :: A : ( s — b ) ( s - c ) , and consequently As ( s - a ) ( s — b ) ( s — c ) , and A = √ ( s ( s — a ) ( s — b ) ( s — c ) ) . PROP ...
... expressed by A , its sides by a , b , and c , and the semiperimeter by s ; then s ( sa ) : A :: A : ( s — b ) ( s - c ) , and consequently As ( s - a ) ( s — b ) ( s — c ) , and A = √ ( s ( s — a ) ( s — b ) ( s — c ) ) . PROP ...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1809 |
Vanlige uttrykk og setninger
ABCD ANALYSIS angle ABC angle ACB angle BAC bisect centre chord circumference COMPOSITION conse consequently the angle decagon describe a circle diameter distance diverging lines draw drawn equal to BC evidently exterior angle fall the perpendicular given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall likewise mean proportional parallel perpendicular point F polygon porism PROB PROP quently radius rectangle rectangle contained regular polygon rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC similar sine square of AC squares of AB tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Populære avsnitt
Side 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Side 28 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Side 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Side 34 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 153 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Side 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...
Side 411 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Side 58 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.
Side 64 - IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 157 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.