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 16
... parallelogram , is one , whose opposite sides are parallel . 36. A square , is one , which has all its sides equal , and all its angles right . contained in the arch BD , as will be more fully explained in the tract on plain ...
... parallelogram , is one , whose opposite sides are parallel . 36. A square , is one , which has all its sides equal , and all its angles right . contained in the arch BD , as will be more fully explained in the tract on plain ...
Seite 45
... parallelogram AD . Cor . 1. - If one angle of a parallelogram be right , the rest are right . For either adjacent angle is right , because it and a right angle are equal to two right angles [ 29. 1 ] ; and the opposite angles are right ...
... parallelogram AD . Cor . 1. - If one angle of a parallelogram be right , the rest are right . For either adjacent angle is right , because it and a right angle are equal to two right angles [ 29. 1 ] ; and the opposite angles are right ...
Seite 46
... parallelogram [ Def . 35 ] . Cor . 6. Two finite right lines [ AB , AC ] , meeting in an angle , being given , to make a parallelogram , whereof they are sides . Through B draw BD parallel to AC , and through C , CD parallel to AB [ 31 ...
... parallelogram [ Def . 35 ] . Cor . 6. Two finite right lines [ AB , AC ] , meeting in an angle , being given , to make a parallelogram , whereof they are sides . Through B draw BD parallel to AC , and through C , CD parallel to AB [ 31 ...
Seite 48
... parallelogram ( Def . 35 ) , and is equal to the parallelogram BD , being on the same base BC , and between the same parallels BC , AH ( 35. 1 ) ; and the paral- lelogram BH is also equal to FH , being on the same base EH , and between ...
... parallelogram ( Def . 35 ) , and is equal to the parallelogram BD , being on the same base BC , and between the same parallels BC , AH ( 35. 1 ) ; and the paral- lelogram BH is also equal to FH , being on the same base EH , and between ...
Seite 50
... parallelogram ( BD ) , and triangle ( BEC ) , be on the same base ( BC ) , and between the same parallels ( BC , AE ) , the parallelogram is double to the triangle . Join CA. The triangle BEC is A equal to BAC 50 BOOK I. EUCLID'S ELEMENTS.
... parallelogram ( BD ) , and triangle ( BEC ) , be on the same base ( BC ) , and between the same parallels ( BC , AE ) , the parallelogram is double to the triangle . Join CA. The triangle BEC is A equal to BAC 50 BOOK I. EUCLID'S ELEMENTS.
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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 |
Häufige Begriffe und Wortgruppen
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...