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
... angle DBC or CBD . A E C B 20. When one right line ( AB ) , standing on another ( CD ) , makes the angles ( ABC , ABD ) on each side of the insisting line ( AB ) equal , each of these equal angles , are called right angles , and the ...
... angle DBC or CBD . A E C B 20. When one right line ( AB ) , standing on another ( CD ) , makes the angles ( ABC , ABD ) on each side of the insisting line ( AB ) equal , each of these equal angles , are called right angles , and the ...
Page 21
... equal [ Ax . 8 ] . And the legs of the angle CAB , coinciding with those of the angle FDE , and those of the angle CBA , with those of the angle FED ; the angles CAB , FDE , as also the angles CBA , FED would coincide , and are therefore ...
... equal [ Ax . 8 ] . And the legs of the angle CAB , coinciding with those of the angle FDE , and those of the angle CBA , with those of the angle FED ; the angles CAB , FDE , as also the angles CBA , FED would coincide , and are therefore ...
Page 22
... angle ADB is equal to BEA , the side DB to AE , and , taking the equals CA , CB , from the equals CD , CE , the side AD to BE [ Ax . 3 ] , therefore the angles DAB , ABE , which are the angles under the base , are equal [ 4. 1 ] . And ...
... angle ADB is equal to BEA , the side DB to AE , and , taking the equals CA , CB , from the equals CD , CE , the side AD to BE [ Ax . 3 ] , therefore the angles DAB , ABE , which are the angles under the base , are equal [ 4. 1 ] . And ...
Page 23
... equal , ( namely AC to AD , and BC to BD ) . For , if possible , let ACB , ADB be such ; and first , let the vertex ... angles BDC , BCD are equal [ 5. 1. ] ; therefore the angle BDC is both equal to , and greater than , the angle BCD ...
... equal , ( namely AC to AD , and BC to BD ) . For , if possible , let ACB , ADB be such ; and first , let the vertex ... angles BDC , BCD are equal [ 5. 1. ] ; therefore the angle BDC is both equal to , and greater than , the angle BCD ...
Page 24
... equal ; the vertical angles ( C , F ) are equal . For the triangle ABC being so applied to the triangle DEF , that the point A may coincide with the point D , and the right line AB with DE , the triangles ABC , DFE being to the same ...
... equal ; the vertical angles ( C , F ) are equal . For the triangle ABC being so applied to the triangle DEF , that the point A may coincide with the point D , and the right line AB with DE , the triangles ABC , DFE being to the same ...
Other editions - View all
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2018 |
Common terms and phrases
angle ACB arch asymptote bisected centre centripetal force circle circumference conical surface conick section described diameter difference directrix distance draw ellipse ellipse or hyperbola equal angles equal Ax equal Cor equal Hyp equiangular Euclid's Elements focus given right line greater half sum inscribed less let fall magnitudes meeting the section opposite hyperbolas opposite sections ordinately applied parabola parallel parallelogram perpendicular plain principal vertex PROB produced PROP proportional proposition quadrant radius rect rectangle right angles right line drawn Scholium secant section or opposite segments semidiameter severally equal shewn sides sine spherical triangle square of CB submultiple tangent THEOR triangle ABC vertex whence
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.