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 NotesCushing and Jewett, 1822 - 494 Seiten |
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Seite 22
... Whence , in the triangles ADB , BEA , the 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 ...
... Whence , in the triangles ADB , BEA , the 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 ...
Seite 26
... whence , EDH being greater than LDH ( Ax . 9 ) , LDF is greater than LDH ; but the angle BAC is equal to LDF ( Hyp . ) , and BAG to LDH ( Hyp . ) , therefore BAC is greater than BAG , which is absurd , BAC being , by supposition , a ...
... whence , EDH being greater than LDH ( Ax . 9 ) , LDF is greater than LDH ; but the angle BAC is equal to LDF ( Hyp . ) , and BAG to LDH ( Hyp . ) , therefore BAC is greater than BAG , which is absurd , BAC being , by supposition , a ...
Seite 29
... whence ACD , being greater than ECF [ Ax . 9 ] , is also greater than its equal A. In like manner , if AC be produced , as to G , the angle BCG may be proved to be greater than ABC ; and therefore ACD , which is equal to BCG ( 15. 1 ) ...
... whence ACD , being greater than ECF [ Ax . 9 ] , is also greater than its equal A. In like manner , if AC be produced , as to G , the angle BCG may be proved to be greater than ABC ; and therefore ACD , which is equal to BCG ( 15. 1 ) ...
Seite 31
... [ 16. 1 ] ; whence , FDG being a right angle , FGE is obtuse , and therefore FEG acute [ Cor . 17. 1 ] , and so FE greater than FG [ 19. 1 ] , or its equal CB . PROP . XX . THEOR . Any two sides ( BOOK I. 31 OF GEOMETRY .
... [ 16. 1 ] ; whence , FDG being a right angle , FGE is obtuse , and therefore FEG acute [ Cor . 17. 1 ] , and so FE greater than FG [ 19. 1 ] , or its equal CB . PROP . XX . THEOR . Any two sides ( BOOK I. 31 OF GEOMETRY .
Seite 33
... whence , FM being greater than FN and less than FH , the point M is between the points N and H in like manner , the point N may be shewn to be between the points D and M : whence , the circles DKM , NKH , being continued lines between ...
... whence , FM being greater than FN and less than FH , the point M is between the points N and H in like manner , the point N may be shewn to be between the points D and M : whence , the circles DKM , NKH , being continued lines between ...
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Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Keine Leseprobe verfügbar - 2018 |
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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
Beliebte Passagen
Seite 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.
Seite 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...
Seite 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.
Seite 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 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...