Easy Introduction to Mathematics, Volum 2Barlett & Newman, 1814 |
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Side
... latter part of The Properties of Numbers , pp . 108 , 109 . 97 Last line , for b = 1.q , read b + 1.q . 123 Dele the third and five following lines . 252 Art . 15. line 2 , dele “ or simple . " 320 The three lines AG , BD , and EC in ...
... latter part of The Properties of Numbers , pp . 108 , 109 . 97 Last line , for b = 1.q , read b + 1.q . 123 Dele the third and five following lines . 252 Art . 15. line 2 , dele “ or simple . " 320 The three lines AG , BD , and EC in ...
Side 1
... latter people , or even Diophantus , ( who is the only Greek writer on the subject at present known , ) understood any thing of the general methods now in use ; accordingly we find but little attempted beyond the solution of nume- rical ...
... latter people , or even Diophantus , ( who is the only Greek writer on the subject at present known , ) understood any thing of the general methods now in use ; accordingly we find but little attempted beyond the solution of nume- rical ...
Side 5
... latter value added to the former in the first equation , and subtracted from it in the second , the results will be s and d . Let us make the experiment . s + d s - d First + 2 namely that x + y = s . 28 2 2 s + d s - d Secondly 2 2 ...
... latter value added to the former in the first equation , and subtracted from it in the second , the results will be s and d . Let us make the experiment . s + d s - d First + 2 namely that x + y = s . 28 2 2 s + d s - d Secondly 2 2 ...
Side 7
... latter , it is the ratio of the lesser inequality , and the given problem is changed into the following ; “ To find a magnitude , from and to which a given magnitude being subtracted and added , the remainder shall be to the sum as r to ...
... latter , it is the ratio of the lesser inequality , and the given problem is changed into the following ; “ To find a magnitude , from and to which a given magnitude being subtracted and added , the remainder shall be to the sum as r to ...
Side 8
... 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 the latter , y = — S b - rx ··· as — sx = b - .8 PART IV . ALGEBRA .
... 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 the latter , y = — S b - rx ··· as — sx = b - .8 PART IV . ALGEBRA .
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volum 2 Charles Butler Uten tilgangsbegrensning - 1814 |
Vanlige uttrykk og setninger
Algebra arithmetical progression axis base bisected called centre chord circle circumference CN² co-sec co-sine co-tan completing the square Conic Sections cube curve diameter distance divided draw EC² equal Euclid Euclid's Elements EXAMPLES.-1 find the numbers former fourth fraction geometrical geometrical progression given equation given ratio greater harmonical mean Hence infinite series inversely last term latter latus rectum less likewise logarithms magnitude method multiplied number of terms odd number parallel parallelogram perpendicular PN² polygon problem Prop proposition Q. E. D. Cor quadrant quotient radius rectangle remainder right angles rule secant shew shewn sides sine solidity straight line substituted subtract tangent theor theorems third triangle unknown quantity VC² versed sine whence wherefore whole numbers x=the
Populære avsnitt
Side 280 - 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.
Side 235 - If two triangles have two sides of the one equal to two sides of the...
Side 247 - 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.
Side 62 - 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.
Side 353 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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. By Theorem II. we have a : b : : sin. A : sin. B.
Side 232 - But things which are equal to the same are equal to one another...
Side 256 - 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.
Side 160 - 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
Side 269 - II. Two magnitudes are said to be reciprocally proportional to two others, when one of the first is to one of the other magnitudes as the remaining one of the last two is to the remaining one of the first.
Side 272 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.