## 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 |

### From inside the book

Page 41

Take any point F within the figure , and draw FA , FB , FC , FD , FE ; there are formed as many triangles as the figure has sides , all the angles of which are

Take any point F within the figure , and draw FA , FB , FC , FD , FE ; there are formed as many triangles as the figure has sides , all the angles of which are

**equal to twice as many right angles as the figure has sides**( by this prop . ) ... Page 42

1 ] ; therefore all the exterior and interior angles of the figure are together

1 ] ; therefore all the exterior and interior angles of the figure are together

**equal to twice as many right angles as the figure has sides**; but the interior angles are equal to twice as many right angles , except four , as the figure ... Page 386

... and all the angles of these triangles are

... and all the angles of these triangles are

**equal to twice as many right angles as the figure has sides**( 32 , 1 Eu . ) , therefore the angles of these triangles which are at their common vertex A , being those which contain the solid ...### 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 - 2018 |

Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2015 |

### 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 2 - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;

Page 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...

Page 42 - 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 176 - If two triangles have an angle of one equal to an angle of the other...

Page 118 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Page 15 - 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 444 - 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 96 - 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 386 - ... 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 49 - Equal triangles on the same base, and on the same side of it, are between the same parallels.