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 20
... equal to the given right line BC . For DH and DE are equal , being radiuses of the same circle EGH [ Def . 10 ] ; taking from them the parts DA , DC , which are equal , being sides of the equilateral triangle ADC , the residues AH , CE ...
... equal to the given right line BC . For DH and DE are equal , being radiuses of the same circle EGH [ Def . 10 ] ; taking from them the parts DA , DC , which are equal , being sides of the equilateral triangle ADC , the residues AH , CE ...
Page 22
... 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 , in the same ...
... 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 , in the same ...
Page 23
... equal , ( namely AC to AD , and BC to BD ) . For , if possible , let ACB , ADB be such ; and first , let the vertex of each fall without the other . C D B Join CD , and because , in the triangle CAD , the sides AC , AD are equal [ Hyp ...
... equal , ( namely AC to AD , and BC to BD ) . For , if possible , let ACB , ADB be such ; and first , let the vertex of each fall without the other . C D B Join CD , and because , in the triangle CAD , the sides AC , AD are equal [ Hyp ...
Page 24
... equal to the two sides ( FD , FE ) of the other , and have also their bases ( AB , DE ) 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 ...
... equal to the two sides ( FD , FE ) of the other , and have also their bases ( AB , DE ) 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 ...
Page 27
... equal , by construction , CG common , and the bases CE , CF equal , being radiuses of the same circle EDF ( Def . 10 ) ; therefore the angles CGE , CGF are equal ( 8. 1 ) , and of course CG is perpendicular to AB ( Def . 20 ) . PROP ...
... equal , by construction , CG common , and the bases CE , CF equal , being radiuses of the same circle EDF ( Def . 10 ) ; therefore the angles CGE , CGF are equal ( 8. 1 ) , and of course CG is perpendicular to AB ( Def . 20 ) . PROP ...
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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 angle square of CB submultiple tangent THEOR triangle ABC vertex whence
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 430 - Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth gravitate towards the earth, and that in proportion to the quantity of matter which they severally contain: that the moon likewise, according to the quantity of its matter, gravitates towards the earth; that, on the other hand, our sea gravitates towards the moon; and all the planets mutually one towards another; and the comets in like manner towards the sun...
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 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 432 - A stone, whirled about in a sling, endeavors to recede from the hand that turns it; and by that endeavor, distends the sling, and that with so much the greater force, as it is revolved with the greater velocity, and as soon as it is let go, flies away.
Page 376 - ... 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 461 - In a parabola, the velocity of a body at any distance from the focus is to the velocity of a body revolving in a circle, at the same distance...
Page 436 - Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say...
Page 127 - D, is said to be Compounded of the ratios of the first to the second, of the second to the third, and so on to the last.
Page 106 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...