## The Canadian Journal of Industry, Science and Art, 5. köide |

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Page 20

... 71h , & c . , degrees , in those cases where the

equations involve a general or variable quantity , but where , in consequence of

relations subsisting between the

to admit ...

... 71h , & c . , degrees , in those cases where the

**coefficients**in the givenequations involve a general or variable quantity , but where , in consequence of

relations subsisting between the

**coefficients**, the roots of the equations happento admit ...

Page 21

For , reduce the function to the form ; where each of the quantities N and D is the

sum of a rational expression , which may be zero , and of a finite series of terms ,

each of them the product of a rational

For , reduce the function to the form ; where each of the quantities N and D is the

sum of a rational expression , which may be zero , and of a finite series of terms ,

each of them the product of a rational

**coefficient**Cor . 1. The Definition implies ... Page 22

... and arrange the terms in N and D according to the powers of Y not exceeding

the ( m - 1 ) " , being the index of the surd Y . Then ata , Y + aYo + . . . tam , I f ( p =

b + by + b2Yo + . . . tbm Y where the

... and arrange the terms in N and D according to the powers of Y not exceeding

the ( m - 1 ) " , being the index of the surd Y . Then ata , Y + aYo + . . . tam , I f ( p =

b + by + b2Yo + . . . tbm Y where the

**coefficients**, b , a , b , a , & c . , may involve ... Page 25

+ A.Y . , where the

of the terms Y ,, Y ,, & c . , is either some power of an integral surd , or the

continued product of several such powers , suppose that no two of the terms , Y ,

Y ,, & c .

+ A.Y . , where the

**coefficients**A , A , & c . , are ( see Def . 1 ) rational , and eachof the terms Y ,, Y ,, & c . , is either some power of an integral surd , or the

continued product of several such powers , suppose that no two of the terms , Y ,

Y ,, & c .

Page 26

( 1 ) can subsist ; where the

zero , are ( see Def . 1 ) rational ; A likewise being rational ; and each of the terms

, U , V , ...... , T , is either some power of an integral surd occurring in f ( P ) , or the

...

( 1 ) can subsist ; where the

**coefficients**, B , C , ...... , E , all of them distinct fromzero , are ( see Def . 1 ) rational ; A likewise being rational ; and each of the terms

, U , V , ...... , T , is either some power of an integral surd occurring in f ( P ) , or the

...

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### Popular passages

Page 127 - I do not know what I may appear to the world ; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Page 119 - Refrain from: these men* and let them alone : for if this counsel or this work be of men, it will come to nought : But if it be of God, ye cannot overthrow it...

Page 61 - My substance was not hid from thee, when I was made in secret, and curiously wrought in the lowest parts of the earth.

Page 122 - Lo, these are parts of his ways: but how little a portion is heard of him? but the thunder of his power who can understand?

Page 66 - To give a stronger impulse and a more systematic direction to scientific inquiry, — to promote the intercourse of those who cultivate Science in different parts of the British Empire, with one another, and with foreign philosophers, — to obtain a more general attention to the objects of Science, and a removal of any disadvantages of a public kind which impede its progress.

Page 13 - The specific gravity of a body is its weight compared with the weight of an equal bulk of pure water. In...

Page 192 - A sight most horrible and disgusting broke upon us as we ascended a sand dune overhanging the little dell in which the pound was built. Within a circular fence 120 feet broad, constructed of the trunks of trees, laced with withes together, and braced by outside supports, lay tossed in every conceivable position over two hundred dead buffalo. From old bulls to calves of three months old, animals of every age were huddled together in all the forced attitudes of violent death.

Page 119 - ... been led to the conclusion that those powers of nature which give rise to races and permanent varieties in animals and plants, are the same as those which in much longer periods produce species, and in a still longer series of ages give rise to differences of generic rank. He appears to me to have succeeded by his investigations and reasonings in throwing a flood of light on many classes of phenomena connected with the affinities, geographical distribution, and geological succession of organic...

Page 370 - Therefore I should infer from analogy that probably all the organic beings which have ever lived on this earth, have descended from some one primordial form, into which life was first breathed.

Page 193 - ... climb to the top of the fence, and, with the hunters who have followed closely in the rear of the buffalo, spear or shoot with bows and arrows or fire-arms at the bewildered animals, rapidly becoming frantic with rage and terror, within the narrow limits of the pound.