## 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 15

A plain angle , is the inclination of two lines to each other in a plain , which meet

together , but are not in the same ... on each side of the insisting line ( AB ) equal ,

each of these

A plain angle , is the inclination of two lines to each other in a plain , which meet

together , but are not in the same ... on each side of the insisting line ( AB ) equal ,

each of these

**equal angles**, are called right angles , and the insisting line , is ... Page 21

Therefore the bases AB , DE are

coinciding with those of the

of the

Therefore the bases AB , DE are

**equal**( Ax . 8 ] . And the legs of the**angle**CAB ,coinciding with those of the

**angle**FDE , and those of the**angle**CBA , with thoseof the

**angle**FED ; the**angles**CAB , FDE , as also the**angles**CBA , FED would ... Page 22

and the angle C is common to both these triangles ; therefore the angle CBD is

equal to CAE , the angle CDB to CEA ... BAE are equal ; which being taken from

the

and the angle C is common to both these triangles ; therefore the angle CBD is

equal to CAE , the angle CDB to CEA ... BAE are equal ; which being taken from

the

**equal angles**CBD , CAE , the residues CBA , CAB , which are the angles at ... Page 23

Join CD , and because , in the triangle CAD , the sides AC , AD are

, the

part BCD A [ Ax . 9 ] , therefore the

Join CD , and because , in the triangle CAD , the sides AC , AD are

**equal**[ Hyp . ], the

**angles**ACD , ADC are**equal**( 5. 1. ] ; but the**angle**ACD is greater than itspart BCD A [ Ax . 9 ] , therefore the

**angle**ADC is greater than BCD , of course ... Page 24

AA If two triangles ( ABC , DEF ) , have the two sides ( CA , CB of one , severally

)

AA If two triangles ( ABC , DEF ) , have the two sides ( CA , CB of one , severally

**equal**to the two sides ( FD , FE ) of the other , and have also their bases ( AB , DE)

**equal**; the vertical**angles**( C , F ) are**equal**. For the triangle ABC being so ...### What people are saying - Write a review

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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...