Easy Introduction to Mathematics, Volumen2Barlett & Newman, 1814 |
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Página 36
... extremes . n = the number of terms d = the common difference of the terms s = the sum of all the terms . -- Then will a + a + d + a + 2d + a + 3d + , & c . to a + n - 1.d be an increasing series of terms in arithmetical progression ...
... extremes . n = the number of terms d = the common difference of the terms s = the sum of all the terms . -- Then will a + a + d + a + 2d + a + 3d + , & c . to a + n - 1.d be an increasing series of terms in arithmetical progression ...
Página 41
... extreme , and s + x = the then by the problem , ( s — x ) 2 + ance 2x2 - a - 3s2 , and x = fres = 4 , s - x = 2 , and s + x = 6 , rs required . thmetical progression , whereof ? , and that of the means 70 ? e common difference ; then ...
... extreme , and s + x = the then by the problem , ( s — x ) 2 + ance 2x2 - a - 3s2 , and x = fres = 4 , s - x = 2 , and s + x = 6 , rs required . thmetical progression , whereof ? , and that of the means 70 ? e common difference ; then ...
Página 41
... extremes is 52 , and that of the means 70 ? Let x = the less extreme , y = the common difference ; then will x , x + y , x + 2y , and x + 3y , represent the progression . Let a = 52 , b = 70 , then by the problem ( x.x + 3y = ) x2 + 3xy ...
... extremes is 52 , and that of the means 70 ? Let x = the less extreme , y = the common difference ; then will x , x + y , x + 2y , and x + 3y , represent the progression . Let a = 52 , b = 70 , then by the problem ( x.x + 3y = ) x2 + 3xy ...
Página 42
... extreme ; then will y - 3 x , y − x , y + -x , and y + 3x = the terms of the progression : wherefore by the problem , y - 3 x.y - x . y + x.y + 3x = p , and y - 3x2 + y - x ) 2 + y + x2 + y + 3x2 = s ; these equations reduced , become ...
... extreme ; then will y - 3 x , y − x , y + -x , and y + 3x = the terms of the progression : wherefore by the problem , y - 3 x.y - x . y + x.y + 3x = p , and y - 3x2 + y - x ) 2 + y + x2 + y + 3x2 = s ; these equations reduced , become ...
Página 63
... extremes , and the two middle terms ( b and c ) the means . 56. Since it has been shewn , ( Art . 27. ) that any ratio is truly expressed by placing its terms in the form of a fraction ; there- fore , when four quantities are ...
... extremes , and the two middle terms ( b and c ) the means . 56. Since it has been shewn , ( Art . 27. ) that any ratio is truly expressed by placing its terms in the form of a fraction ; there- fore , when four quantities are ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 235 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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.
Página 232 - But things which are equal to the same are equal to one another...
Página 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.
Página 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
Página 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.
Página 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.