## 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 42

... at its other extreme ( D ) , by right lines ( DA , DB ) drawn to the extremes ( A , B ) of the base , is equal to

... at its other extreme ( D ) , by right lines ( DA , DB ) drawn to the extremes ( A , B ) of the base , is equal to

**half**the vertical angle ( ACB ) . Page 43

and CDB equal to the

and CDB equal to the

**half**of ACB [ Hyp . ] , CBD is also the**half**of ACB ; therefore the angles CBD , CDB are equal [ Ax . 7 ) , and therefore CD is equal ... Page 44

10 ] , the angle AGB is

10 ] , the angle AGB is

**half**of ACB [ by last Cor . ] , ' but ADB is also**half**ACE equal ( Ax . 7 , the external angle AGB of the triangle GBD to 2 ( Hyp . ] ... Page 55

1 ) , either of them , as ABD , is

1 ) , either of them , as ABD , is

**half**a right angle ; and , in the triangle CBG , the angle BCG is equal to the internal remote on the same side A ( 29. Page 62

The square of a right line , is four - fold the square of its

The square of a right line , is four - fold the square of its

**half**. For , a right line being bisected , the rectangle under the parts , is equal to the ...### 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 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 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 172 - If two triangles have an angle of one equal to an angle of the other...

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

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 440 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Page 94 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another.

Page 382 - ... 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 47 - Equal triangles on the same base, and on the same side of it, are between the same parallels.