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
Results 1-5 of 39
Page 29
... interior remote angle B ( 16. 1 ) ; adding to each the angle ACB , the angles ACD , ACB together , are greater than the angles B and A B • D • ACB together [ Ax . 4 ] ; but 5 BOOK I. 29 OF GEOMETRY . to AED, DEB together (Theor. at 11. ...
... interior remote angle B ( 16. 1 ) ; adding to each the angle ACB , the angles ACD , ACB together , are greater than the angles B and A B • D • ACB together [ Ax . 4 ] ; but 5 BOOK I. 29 OF GEOMETRY . to AED, DEB together (Theor. at 11. ...
Page 32
... adding to each EC , the right lines BA and AC , are greater than BE and EC [ Ax . 4 ] ; but the sides DE , EC of the triangle DEC , are great- er than the remaining side DC ( 20. 1 ) , therefore , adding to each BD , the right lines BE ...
... adding to each EC , the right lines BA and AC , are greater than BE and EC [ Ax . 4 ] ; but the sides DE , EC of the triangle DEC , are great- er than the remaining side DC ( 20. 1 ) , therefore , adding to each BD , the right lines BE ...
Page 39
... adding to each BGH , the angles BGH , GHD together , are equal to AGH , BGH to- gether [ Ax . 2. ] , but AGH , BGH together are equal to two right angles [ 13. 1 ] , therefore BGH , GHD together are equal to two right angles . Theorem ...
... adding to each BGH , the angles BGH , GHD together , are equal to AGH , BGH to- gether [ Ax . 2. ] , but AGH , BGH together are equal to two right angles [ 13. 1 ] , therefore BGH , GHD together are equal to two right angles . Theorem ...
Page 53
... adding to each the angle GHK , the angles GHM , GHK together , are equal to K and GHK together ( Ax . 2 ) ; but the angles K and GHK together , are equal to two right angles ( 29. 1 ) , therefore the angles GHM , GHK together , are ...
... adding to each the angle GHK , the angles GHM , GHK together , are equal to K and GHK together ( Ax . 2 ) ; but the angles K and GHK together , are equal to two right angles ( 29. 1 ) , therefore the angles GHM , GHK together , are ...
Page 55
... adding to each the angle ABC , the angles FBC , ABD are equal ( Ax . 2 ) , and the sides FB , BC are severally equal to the sides AB , BD ( Def . 36 ) , therefore the triangles FBC , ABD are equal ( 4. 1 ) ; but the parallelogram FA is ...
... adding to each the angle ABC , the angles FBC , ABD are equal ( Ax . 2 ) , and the sides FB , BC are severally equal to the sides AB , BD ( Def . 36 ) , therefore the triangles FBC , ABD are equal ( 4. 1 ) ; but the parallelogram FA is ...
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 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...