## 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 ix

In the fifth book of Euclid's Elements ,

In the fifth book of Euclid's Elements ,

**proportional**magnitudes are defined by submultiples , instead of Euclid's method by multiples ; as this definition ... Page 129

Three magnitudes , are said to be

Three magnitudes , are said to be

**proportional**, when the first has the same ratio to the second , as the second has to the third . 10. Page 130

Inverting ; when it is inferred , if four magnitudes be

Inverting ; when it is inferred , if four magnitudes be

**proportional**, that the second is to the first , as the fourth to the third ; as is shewn in Theor . Page 136

If there be four

If there be four

**proportional**magnitudes ( AB , CD , AB I I -- K EF , GH ) , and equimul- X Ꭲ Ꭱ tiples ( IK , NO ) of the CID L - 1-1-1 M antecedents ( AB ... Page 138

... four magnitudes Aof the same kind , be equal to the third ( C ) , and BEthe second ( B ) , to the fourth ( D ) ; the magni- C. tudes are

... four magnitudes Aof the same kind , be equal to the third ( C ) , and BEthe second ( B ) , to the fourth ( D ) ; the magni- C. tudes are

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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.