Easy Introduction to Mathematics, Volumen2Barlett & Newman, 1814 |
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Página 19
... Multiplying eq . 3. into b . 3xb 4x = bm- d xy Involving equation 2 . 2 & 5 - = n ' . с Multiplying eq . 5. into c . 5XC Dividing equation 6. by y . 6 + y Equating the 4th and 7th steps . 4 = 7 8 bm- 6 xy = cn2 . 7x = сп - y by cn = d y ...
... Multiplying eq . 3. into b . 3xb 4x = bm- d xy Involving equation 2 . 2 & 5 - = n ' . с Multiplying eq . 5. into c . 5XC Dividing equation 6. by y . 6 + y Equating the 4th and 7th steps . 4 = 7 8 bm- 6 xy = cn2 . 7x = сп - y by cn = d y ...
Página 21
... multiplied into the less , produces 75 ; and the square of the less multiplied into the greater , 45 : what are the numbers ? Let x = the greater , y = the less , a = 75 , b = 45 ; then x2y = a , and xy = b , by the problem ; divide the ...
... multiplied into the less , produces 75 ; and the square of the less multiplied into the greater , 45 : what are the numbers ? Let x = the greater , y = the less , a = 75 , b = 45 ; then x2y = a , and xy = b , by the problem ; divide the ...
Página 35
... multiplying the sum of the next preceding powers by s , and from this product subtracting the sum of the powers next preceding those multi- plied by p . Thus , the sum of the 4th powers sx sum D 2 PART IV . 35 GENERAL PROBLEMS .
... multiplying the sum of the next preceding powers by s , and from this product subtracting the sum of the powers next preceding those multi- plied by p . Thus , the sum of the 4th powers sx sum D 2 PART IV . 35 GENERAL PROBLEMS .
Página 41
... sub- nation , and it becomes x2 + 9x 81 9 btain x = √at = 4 : umbers required . 4 2 thmetical progression is 48 , multiplied into the less ex- er of terms ; required the terms 10 , being given , to find the first CAL PROGRESSION . 41.
... sub- nation , and it becomes x2 + 9x 81 9 btain x = √at = 4 : umbers required . 4 2 thmetical progression is 48 , multiplied into the less ex- er of terms ; required the terms 10 , being given , to find the first CAL PROGRESSION . 41.
Página 41
... is 48 , and if the common difference d be multiplied into the less ex- treme , the product equals the number of terms ; required the terms of the progression ? 6 Let a = the first term , then da PART IV . 41 ARITHMETICAL PROGRESSION .
... is 48 , and if the common difference d be multiplied into the less ex- treme , the product equals the number of terms ; required the terms of the progression ? 6 Let a = the first term , then da PART IV . 41 ARITHMETICAL PROGRESSION .
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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.