## Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N. Bosworth assisted by other gentlemen of eminence, Volume 5 |

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For , let : absciss have the

For , let : absciss have the

**ratio**to each other , not of the two right lines , DE and FG , move parallel to ordinate and absciss , but of the ordinate and sub- themselves from two other right lines , BA and tangent ; and , of ... Page 7

Mr. Euler , in his calculations , supposes

Mr. Euler , in his calculations , supposes

**ratio**of tbe vis vita of the striking body , of the the bardness of a body to be proportional to the hardness , and of the plane of contact . But if M , force or pressure requisite to make a ... Page 9

If a body be moved from quiescence , through if m denote the motive force , the same space by different forces , the velocities and b the body , or its weight , generated will be in a subduplicate

If a body be moved from quiescence , through if m denote the motive force , the same space by different forces , the velocities and b the body , or its weight , generated will be in a subduplicate

**ratio**of the and f the accelerating or ... Page 15

Its extremes are two sounds in the

Its extremes are two sounds in the

**ratio**right again , will be made to play , by putting of 4 : 3. ... to their forin posed of the**ratios**of 27 : 20 , and of 4 : 5 . and situation , as pyramidal fountain , bason FO'URTHLY . ad . Page 15

And hence there may be innumerable fractions all of the same value , as there may be those of the common form by an easy application These continued fractions may be reduced to innumerable quantities all in the same

And hence there may be innumerable fractions all of the same value , as there may be those of the common form by an easy application These continued fractions may be reduced to innumerable quantities all in the same

**ratio**, viz . of the ...### What people are saying - Write a review

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according acid ancient angles appear applied ball barrel becomes body born botany called cause church circle colour common considerable consists contained continued covered died divided Dryden earth effect employed English equal experiments expressed feet figure fire force four French gass give given glass gold grains greater ground half head heat horses inches increase iron Italy kind known language Latin leaves length less lower manner matter means mercury metal method motion nature observed pass person piece plants principal probability produced Prop proportion quantity ratio received remains respect river says Shakspeare side sometimes species straight line supposed surface taken term Theor thing third tion town trees weight whole

### Popular passages

Page 151 - How many things are there which a man cannot, with any face or comeliness, say or do himself! A man can scarce allege his own merits with modesty, much less extol them ; a man cannot sometimes brook to supplicate or beg; and a number of the like. But all these things are graceful in a friend's mouth, which are blushing in a man's own.

Page 151 - Men have their time, and die many times in desire of some things which they principally take to heart; the bestowing of a child, the finishing of a work, or the like. If a man have a true friend, he may rest almost secure that the care of those things will continue after him.

Page 89 - If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 83 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle which is contained by the two sides...

Page 95 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Page 85 - ... subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn perpendicular to BC produced.

Page 85 - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.

Page 89 - A greater magnitude is said to be a multiple of a less, when the greater is measured by the less ; that is, ' when the greater contains the less a certain number of times exactly.' 3. ' Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.