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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Αποτελέσματα 1 - 5 από τα 44.
Σελίδα 24
... remaining angles FDE , FED of the triangle DFE , and also the triangles themselves . PROP . IX . PROB . To bisect , or divide into two equal parts , a given rectili- lineal angle ( BAC ) . Take any point D in AB , and , on AC , take AE ...
... remaining angles FDE , FED of the triangle DFE , and also the triangles themselves . PROP . IX . PROB . To bisect , or divide into two equal parts , a given rectili- lineal angle ( BAC ) . Take any point D in AB , and , on AC , take AE ...
Σελίδα 28
... remaining angles ABE , ABD are equal ( Ax . 3 ) , part and whole , which is absurd ( Ax . 9 ) : therefore BE is not the continuation of CB . In like manner it may be shewn , that no other right line , but BD , can be the continuation of ...
... remaining angles ABE , ABD are equal ( Ax . 3 ) , part and whole , which is absurd ( Ax . 9 ) : therefore BE is not the continuation of CB . In like manner it may be shewn , that no other right line , but BD , can be the continuation of ...
Σελίδα 29
... remaining angles AEC and DEB are equal ( Ax . 3 ) . In like manner , the angles AED , CEB may be proved equal . Cor . Two intersecting right lines ( AB , CD ) , make an- gles , equal to four right angles . Cor . 2 - If more right lines ...
... remaining angles AEC and DEB are equal ( Ax . 3 ) . In like manner , the angles AED , CEB may be proved equal . Cor . Two intersecting right lines ( AB , CD ) , make an- gles , equal to four right angles . Cor . 2 - If more right lines ...
Σελίδα 32
... remaining side ( BC ) . On either of the sides to be prov- ed greater than the remaining one , as BA , produced , take AD equal to the other AC , and join CD . B A C The angles D and ACD at the base of the isosceles triangle ACD are ...
... remaining side ( BC ) . On either of the sides to be prov- ed greater than the remaining one , as BA , produced , take AD equal to the other AC , and join CD . B A C The angles D and ACD at the base of the isosceles triangle ACD are ...
Σελίδα 33
... remaining one , to make a triangle having its sides severally equal to these right lines . D FNGMHE A At any point D , put the right line DF equal to A ( 2. 1 ) , on which produced take FG equal to B , and GH to C ( 3. 1 ) ; from the ...
... remaining one , to make a triangle having its sides severally equal to these right lines . D FNGMHE A At any point D , put the right line DF equal to A ( 2. 1 ) , on which produced take FG equal to B , and GH to C ( 3. 1 ) ; from the ...
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...