Easy Introduction to Mathematics, Volume 2Barlett & Newman, 1814 |
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Page 4
... manner of converting any particular numericał problem into a general form , and of substituting and deriving expressions for the unknown quantities , in a great variety of ways , are shewn and explained . PROBLEM 1. Given the sum and ...
... manner of converting any particular numericał problem into a general form , and of substituting and deriving expressions for the unknown quantities , in a great variety of ways , are shewn and explained . PROBLEM 1. Given the sum and ...
Page 37
... manner , by equating the values of a in theorems 2 s 2 and 6 , ( viz . z — n — 1.d = 23 — z , ) we derive z = n n S ... manner . 18. The following is a synopsis of the whole doctrine of arithmetical progression , wherein all the theorems ...
... manner , by equating the values of a in theorems 2 s 2 and 6 , ( viz . z — n — 1.d = 23 — z , ) we derive z = n n S ... manner . 18. The following is a synopsis of the whole doctrine of arithmetical progression , wherein all the theorems ...
Page 43
... manner , 1 × 2 × 3 × 4x5x6 5 things admit of 1 × 2 × 3 × 4x5 permutat utations 6 .... 7 & c . 1 × 2 × 3 × 4 × 5 × 6 × 7 . & c . And therefore n things admit of 1x2x3 , & c . to n , permutations . EXAMPLES . - 1 . How many ways can the ...
... manner , 1 × 2 × 3 × 4x5x6 5 things admit of 1 × 2 × 3 × 4x5 permutat utations 6 .... 7 & c . 1 × 2 × 3 × 4 × 5 × 6 × 7 . & c . And therefore n things admit of 1x2x3 , & c . to n , permutations . EXAMPLES . - 1 . How many ways can the ...
Page 44
... manner be formed ; and if c , d , e , & c . be placed respectively before each of the rest , n - 1 permutations in each case will arise ; consequently , if each of the n things be placed before all the rest , there will be formed in the ...
... manner be formed ; and if c , d , e , & c . be placed respectively before each of the rest , n - 1 permutations in each case will arise ; consequently , if each of the n things be placed before all the rest , there will be formed in the ...
Page 50
... manner , if the terms of the ratio a : b , or α — be both multiplied by any quantity n , the resulting ratio an : b bn , or an is the same as a : b , or and the same in general . bn # 30. Hence , one ratio is greater than another , 50 ...
... manner , if the terms of the ratio a : b , or α — be both multiplied by any quantity n , the resulting ratio an : b bn , or an is the same as a : b , or and the same in general . bn # 30. Hence , one ratio is greater than another , 50 ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 235 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 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.
Page 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.
Page 232 - But things which are equal to the same are equal to one another...
Page 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.
Page 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
Page 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.
Page 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.