An Easy Introduction to the Mathematics: In which the Theory and Practice are Laid Down and Familiarly Explained ... A Complete and Easy System of Elementary Instruction in the Leading Branches of the Mathematics; ... Adapted to the Use of Schools, Junior Students at the Universities, and Private Learners, Especially Those who Study Without a Tutor. In Two Volumes, Volumen2Bartlett and Newman ; [etc., etc..], 1814 |
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Página 3
... assumed have the properties described in the problem , is called the SYNTHESIS , Or SYNTHETICAL DEMONSTRATION of the problem , and frequently the COMPOSITION . 9. When the value of any quantity , which was at first un- known , is found ...
... assumed have the properties described in the problem , is called the SYNTHESIS , Or SYNTHETICAL DEMONSTRATION of the problem , and frequently the COMPOSITION . 9. When the value of any quantity , which was at first un- known , is found ...
Página 79
... assumed , so that A = mB , or m m B b A = , then will amb , or a = - respectively . m m 110. If the corresponding values of A and B be known , then will the value of the constant quantity m be likewise known . For if a and b be the ...
... assumed , so that A = mB , or m m B b A = , then will amb , or a = - respectively . m m 110. If the corresponding values of A and B be known , then will the value of the constant quantity m be likewise known . For if a and b be the ...
Página 127
... assumed magnitudes . COR . Hence , any magnitude is greater than the greatest root of the equation , which , being substituted for the unknown quan- tity , gives a positive result . 45. To find a limit greater than the greatest root of ...
... assumed magnitudes . COR . Hence , any magnitude is greater than the greatest root of the equation , which , being substituted for the unknown quan- tity , gives a positive result . 45. To find a limit greater than the greatest root of ...
Página 131
... assumed , viz . + 2 , is one of the roots of the original equation , ( Art . 33. note , ) and the transformed equation being divisible by y , will thereby be reduced one dimension lower : thus , y3 + 4y2 — 19y + 14 = 0 ; the divisors of ...
... assumed , viz . + 2 , is one of the roots of the original equation , ( Art . 33. note , ) and the transformed equation being divisible by y , will thereby be reduced one dimension lower : thus , y3 + 4y2 — 19y + 14 = 0 ; the divisors of ...
Página 132
... assumed progression , by the common difference of the terms of the former ; and if the progression be increas- ing , prefix the sign + to the quotient ; but if it be decreasing , prefix the sign : this quotient will be a root of the ...
... assumed progression , by the common difference of the terms of the former ; and if the progression be increas- ing , prefix the sign + to the quotient ; but if it be decreasing , prefix the sign : this quotient will be a root of the ...
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Términos y frases comunes
Algebra arithmetical progression base biquadratic equation bisected called centre chord circle circumference CN² co-sec co-sine co-tan common compasses Conic Sections conjugate hyperbola cube cubic equation curve described diameter difference distance divided draw drawn EC² ellipse equal equiangular Euclid EUCLID'S ELEMENTS EXAMPLES.-1 former fourth Geometry given equation given ratio given straight line greater Hence hyperbola infinite series latter latus rectum likewise logarithms magnitude measure method multiplied odd number parabola parallel parallelogram perpendicular plane PN² polygon problem Prop proposition Q. E. D. Cor quadrant quotient radius rectilineal figures right angles roots rule scale secant segments shewn sides sine square substituted subtracted tangent theor theorems third unknown quantity VC² versed sine whence wherefore whole numbers
Pasajes populares
Página 320 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Página 405 - 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.
Página 287 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 66 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Página 272 - But things which are equal to the same are equal to one another (Ax.
Página 267 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Página 263 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 281 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 294 - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Página 190 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of