## 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 |

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Page 11

The ancients considered these figures , as

with the surface of a cone ; which intersection

in this work defined under this name , as is demonstrated in the five last ...

The ancients considered these figures , as

**produced**by the intersection of a plainwith the surface of a cone ; which intersection

**produces**the same figures , as arein this work defined under this name , as is demonstrated in the five last ...

Page 17

That a terminated right line , may be

from any point as a centre , at any distance from that centre , a circle may be

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. Thatfrom any point as a centre , at any distance from that centre , a circle may be

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

each ...

Page 18

... be so

together are least , as to meet . See note to Prop . 29th of this book .

PROPOSITION I. PROBLEM . A Upon a given might finite 18 BOOK I. EUCLID'S

ELEMENTS.

... be so

**produced**towards the part ( B , D ) , on which the interior angles takentogether are least , as to meet . See note to Prop . 29th of this book .

PROPOSITION I. PROBLEM . A Upon a given might finite 18 BOOK I. EUCLID'S

ELEMENTS.

Page 19

D. Then , since the point C is without the circle AED , and the point B within the

same circle , and the circles BEC , AED , are continued lines on each side of the ...

**Produce**AB both ways ( post . 2 ) , so as to meet these circles in the points C andD. Then , since the point C is without the circle AED , and the point B within the

same circle , and the circles BEC , AED , are continued lines on each side of the ...

Page 21

The angles ( CAB , CBA ) , at the base ( AB ) of an isosceles triangle ( ABC ) , are

equal : and , if the equal sides ( CA , CB ) be

angles under the base ( BAD , ABE are equal . . B D In either leg , as CA , BOOK I

. OF ...

The angles ( CAB , CBA ) , at the base ( AB ) of an isosceles triangle ( ABC ) , are

equal : and , if the equal sides ( CA , CB ) be

**produced**below the base , theangles under the base ( BAD , ABE are equal . . B D In either leg , as CA , BOOK I

. OF ...

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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...