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, Volume 2Bartlett and Newman ; [etc., etc..], 1814 - Mathematics |
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Page 3
... respective unknown quantity in the given equations ; that is , by reasoning in an order the converse of analysis , and there- by ultimately proving that the quantities thus assumed have the properties described in the problem , is ...
... respective unknown quantity in the given equations ; that is , by reasoning in an order the converse of analysis , and there- by ultimately proving that the quantities thus assumed have the properties described in the problem , is ...
Page 5
... respectively , then those values being substituted for x and y in the given equations , and the latter value added to the former in the first équation , and subtracted from it in the second , the results will be s and d . Let us make ...
... respectively , then those values being substituted for x and y in the given equations , and the latter value added to the former in the first équation , and subtracted from it in the second , the results will be s and d . Let us make ...
Page 8
... respectively , r = the multiplier of x , s = the multiplier of y , and b the sum of the multiples of x and y ; then by the pro- blem , x + y = a , and rx + sy = b . From the first of these equations , b - rx we have y = a - x ; and from ...
... respectively , r = the multiplier of x , s = the multiplier of y , and b the sum of the multiples of x and y ; then by the pro- blem , x + y = a , and rx + sy = b . From the first of these equations , b - rx we have y = a - x ; and from ...
Page 11
... respectively ; then by the problem , xy = p , and X Y = q ; from the latter , x = qy ; this substituted for x in the former , gives qyo = p ' : ' y2 = " , P and y = √ ; x = qy = ५ SYNTHESIS . First , √pqx Ρ = √pq , Q. E. I. q q p ...
... respectively ; then by the problem , xy = p , and X Y = q ; from the latter , x = qy ; this substituted for x in the former , gives qyo = p ' : ' y2 = " , P and y = √ ; x = qy = ५ SYNTHESIS . First , √pqx Ρ = √pq , Q. E. I. q q p ...
Page 28
... respectively . 39. To find a point in the straight line which joins two lumi- naries , or in the line produced , which is equally enlightened by both " . Let a their distance apart , x = the distance of the least of them from the ...
... respectively . 39. To find a point in the straight line which joins two lumi- naries , or in the line produced , which is equally enlightened by both " . Let a their distance apart , x = the distance of the least of them from the ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 272 - But things which are equal to the same are equal to one another (Ax.
Page 267 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Page 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.
Page 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.
Page 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.
Page 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