## Euclid's Elements of Geometry: The Six First Books. To which are Added, Elements of Plain and Spherical Trigonometry, a System of Conick Sections, Elements of Natural Philosophy, as Far as it Relates to Astronomy, According to the Newtonian System, and Elements of Astronomy: with Notes |

### From inside the book

Results 1-5 of 100

Page 14

A figure , is that which is inclosed by one or more boundaries . 10. A circle , is a

plain figure , bounded by one line ( ADBA ) , cvery where equally distant from a

point ( C ) within it . D 8 B в C 11. That point ( C ) , is called the

.

A figure , is that which is inclosed by one or more boundaries . 10. A circle , is a

plain figure , bounded by one line ( ADBA ) , cvery where equally distant from a

point ( C ) within it . D 8 B в C 11. That point ( C ) , is called the

**centre**of the circle.

Page 17

That a terminated right line , may be produced at pleasure in a right line . 3. That

from any point as a

described . AXIOMS . 1. Things , which are equal to the same thing , are equalt )

each ...

That a terminated right line , may be produced at pleasure in a right line . 3. That

from any point as a

**centre**, at any distance from that**centre**, a circle may bedescribed . AXIOMS . 1. Things , which are equal to the same thing , are equalt )

each ...

Page 19

From the

the

both ways ( post . 2 ) , so as to meet these circles in the points C and D. Then ...

From the

**centre**A , at the distance AB , describe the circle BEC ( post . 3 ) . Fromthe

**centre**B , at the distance BA , describe the circle AED ( post . 3 ) . Produce ABboth ways ( post . 2 ) , so as to meet these circles in the points C and D. Then ...

Page 33

1 ) ; from the

and C , or their equals FM , NG together , are greater than B or FG ( Hyp ...

1 ) ; from the

**centre**F , at the distance FD , describe the circle DKM , and from the**centre**G , at the distance GH , describe the circle NKH [ Post . 3 ] ; and , since Aand C , or their equals FM , NG together , are greater than B or FG ( Hyp ...

Page 80

A right line , is said to be inscribed in a circle , when its extremes are in the

circumfe . rence of the circle . 4. Right lines , are said to be equally distant from

the

equal .

A right line , is said to be inscribed in a circle , when its extremes are in the

circumfe . rence of the circle . 4. Right lines , are said to be equally distant from

the

**centre**of a circle , when the perpendiculars drawn to them from the**centre**areequal .

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2015 |

Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2017 |

### Common terms and phrases

adding applied arch axis base bisected body centre circle circumference common compounded conick section Constr contained contrary course described diameter difference directrix distance double draw drawn ellipse equal equal angles equiangular extremes figure focus force formed four given greater half hyperbola inscribed join legs less let fall magnitudes manner meet motion opposite ordinate parabola parallel parallelogram parameter passing perpendicular plain principal produced PROP proportional proposition proved radius ratio rectangle remaining right angles right line secant segments shewn sides similar sine square taken tangent THEOR third touching triangle ABC unequal vertex whence whole

### Popular passages

Page 40 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 428 - Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth gravitate towards the earth, and that in proportion to the quantity of matter which they severally contain: that the moon likewise, according to the quantity of its matter, gravitates towards the earth; that, on the other hand, our sea gravitates towards the moon; and all the planets mutually one towards another; and the comets in like manner towards the sun...

Page 13 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Page 430 - A stone, whirled about in a sling, endeavors to recede from the hand that turns it; and by that endeavor, distends the sling, and that with so much the greater force, as it is revolved with the greater velocity, and as soon as it is let go, flies away.

Page 374 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Page 459 - In a parabola, the velocity of a body at any distance from the focus is to the velocity of a body revolving in a circle, at the same distance...

Page 434 - Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say...

Page 127 - D, is said to be Compounded of the ratios of the first to the second, of the second to the third, and so on to the last.

Page 106 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...