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 σελίδες |
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Σελίδα 21
... same part ; the point A would coincide with the point D , for part of CA cannot coincide with FD , and part be without it , as in the direction GH , ' for then two ... triangles themselves would coincide , and are therefore equal [ Ax . 8 ] ...
... same part ; the point A would coincide with the point D , for part of CA cannot coincide with FD , and part be without it , as in the direction GH , ' for then two ... triangles themselves would coincide , and are therefore equal [ Ax . 8 ] ...
Σελίδα 50
... triangles ABC , EBC , being on the same base BC , and between the same ... no other right line drawn through A. except AD , is parallel to BC ; therefore AD ... side . DE of the triangle DEF , in a point G different from the vertex , and ...
... triangles ABC , EBC , being on the same base BC , and between the same ... no other right line drawn through A. except AD , is parallel to BC ; therefore AD ... side . DE of the triangle DEF , in a point G different from the vertex , and ...
Σελίδα 81
... two radiuses , and the part of the circumference between them . 11. Similar ... No other point in EC , but F , can be the centre , for , if it were , the radiuses ... triangles GDA , GDB , the side DA is equal to DB ( Constr . ) , DG common ...
... two radiuses , and the part of the circumference between them . 11. Similar ... No other point in EC , but F , can be the centre , for , if it were , the radiuses ... triangles GDA , GDB , the side DA is equal to DB ( Constr . ) , DG common ...
Σελίδα 82
... Two right lines inscribed in a circle , cutting each other , and not passing ... cannot bi- sect each other ; for let them , if possible , do it , and find the centre of the ... equal to FEC , the part to the 82 BOOK III . EUCLID'S ELEMENTS.
... Two right lines inscribed in a circle , cutting each other , and not passing ... cannot bi- sect each other ; for let them , if possible , do it , and find the centre of the ... equal to FEC , the part to the 82 BOOK III . EUCLID'S ELEMENTS.
Σελίδα 84
... there can be drawn to the circumference , but two right lines ( as DF , DH ) ... triangles BCD , ECD , the sides BC , CD are severally equal to the sides EC ... cannot be drawn from that point to the circumference . For however three right ...
... there can be drawn to the circumference , but two right lines ( as DF , DH ) ... triangles BCD , ECD , the sides BC , CD are severally equal to the sides EC ... cannot be drawn from that point to the circumference . For however three right ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...