The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 10
... perpendicular to it . XI . An obtufe angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is ...
... perpendicular to it . XI . An obtufe angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is ...
Σελίδα 23
... perpendicular to AB from the point C. Take any point D upon the other fide of AB , and from the centre C , at the distance CD , defcribe the circle EGF C a Book I. 10. Def . 1 . E H b 3. Poft . meeting AB in F , G ; and bi- A F G B D ...
... perpendicular to AB from the point C. Take any point D upon the other fide of AB , and from the centre C , at the distance CD , defcribe the circle EGF C a Book I. 10. Def . 1 . E H b 3. Poft . meeting AB in F , G ; and bi- A F G B D ...
Σελίδα 63
... perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Let ABC be an obtufe angled triangle , having the obtufe angle ACB , and from the point A let AD be drawn ...
... perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Let ABC be an obtufe angled triangle , having the obtufe angle ACB , and from the point A let AD be drawn ...
Σελίδα 64
... perpendicular let fall upon it from the oppo- fite angle , and the acute angle . a Let ABC be any triangle , and the angle at B one of its a cute angles , and upon BC , one of the fides containing it , let fall the perpendicular AD from ...
... perpendicular let fall upon it from the oppo- fite angle , and the acute angle . a Let ABC be any triangle , and the angle at B one of its a cute angles , and upon BC , one of the fides containing it , let fall the perpendicular AD from ...
Σελίδα 65
... perpendicular to BC ; then is BC the ftraight line between the perpendicular and the acute angle at B ; and it is manifeft that the fquares of AB , BC are e- qual to the fquare of AC , and twice the fquare of BC : Therefore , in every ...
... perpendicular to BC ; then is BC the ftraight line between the perpendicular and the acute angle at B ; and it is manifeft that the fquares of AB , BC are e- qual to the fquare of AC , and twice the fquare of BC : Therefore , in every ...
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The First Six Books: Together with the Eleventh and Twelfth Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
added alfo alſo altitude angle ABC angle BAC bafe baſe becauſe bifected Book Book XI centre circle circle ABCD circumference common cone cylinder defcribed definition demonftrated diameter divided double draw drawn equal equal angles equiangular equimultiples excefs fame fame multiple fecond fegment fhall fides fimilar firft folid folid angle fore four fourth fquare fquare of AC ftraight line given angle given in fpecies given in pofition given magnitude given ratio greater Greek half join lefs magnitude meet oppofite parallel parallelogram perpendicular plane prifms produced PROP propofition proportionals pyramid rectangle rectangle contained remaining right angles Take taken thefe THEOR theſe third triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 474 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Σελίδα 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Σελίδα 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 62 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Σελίδα 200 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.