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

### From inside the book

Results 6-10 of 16

Page 91

**Prop**. II . Theor . If any two points be taken in angle with the diameter at its extremity , or so the circumference of a circle , the straight line small ... Page 93

**Prop**. Iil . Prob . About a given circle to describe 10. ... equiangular to a given triangle . the first is said to have to the third the duplicate**Prop**. Page 95

**Prop**. of this Book V. and if of the first and third there be taken equi14. Invertendo , by inversion : when there are multiples , these shall be ... Page 97

**Prop**. XI . Theor . Ratios that are the same to fourth ; and the fifth to the second , the same ratin the same ratio , are the same to one another . which ... Page 99

If the outward angle of a tri- the four straight lines are proportionals . angle made by producing one of its sides , be di-

If the outward angle of a tri- the four straight lines are proportionals . angle made by producing one of its sides , be di-

**Prop**. XVII . Theor .### What people are saying - Write a review

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### 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.