## 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 129

The ratio of the first , of any number of magnitudes of the same kind , to the last , is said to be

The ratio of the first , of any number of magnitudes of the same kind , to the last , is said to be

**compounded**, of the ratios of the first to the second ... Page 130

**Compounding**; when it is inferred , if four magnitudes be proportional , that the first and second together is to the second , as the third and fourth ... Page 153

... and therefore , that , “ ratios

... and therefore , that , “ ratios

**compounded**of equal 66 ratios ( see Def . 13. 5 ) , however disposed , are equal . " PROP . XXIV . THEOR . Page 154

5 ) ; therefore , by

5 ) ; therefore , by

**compounding**, AK is to BK , as EL to FL ( 18. 5 ) , G -- H and therefore , BK being to CD ... Page 159

6 ] , and , by

6 ] , and , by

**compounding**, AC is to CE or its equal CB , as AD is to BD ( 18. 5 ] . Part 2. The same construction remaining , AD is to BD , as AC to CB ...### What people are saying - Write a review

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### 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 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.