The First Six Books: Together with the Eleventh and Twelfth |
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Side 21
There . b . s . Ax • fore if two triangles , & c . Q. E. D. T PROP . IX . PROB . O bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rect lineal angle , it is required to bi- fect it ...
There . b . s . Ax • fore if two triangles , & c . Q. E. D. T PROP . IX . PROB . O bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rect lineal angle , it is required to bi- fect it ...
Side 22
P R O B. C D. B O draw a ftraight line at right angles to a given ftraight line , from a given point in the fame . TRfr Let AB be a given ftraight line , and C a point given in it ; it is required to draw a ftraight line from the point ...
P R O B. C D. B O draw a ftraight line at right angles to a given ftraight line , from a given point in the fame . TRfr Let AB be a given ftraight line , and C a point given in it ; it is required to draw a ftraight line from the point ...
Side 23
line , the angle CBE is equal a to the angle EBA ; in the fame manner , because ABD is a ftraight line , the angle DBE is ... E D B PROB . draw a ftraight line to a Tftraight line of an unlimited length , from a given point without it .
line , the angle CBE is equal a to the angle EBA ; in the fame manner , because ABD is a ftraight line , the angle DBE is ... E D B PROB . draw a ftraight line to a Tftraight line of an unlimited length , from a given point without it .
Side 30
Ta given point in a given ftraight line , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given ftraight line , and A the given point in it , and DCE the given rectilineal angle ; it is required to make an ...
Ta given point in a given ftraight line , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given ftraight line , and A the given point in it , and DCE the given rectilineal angle ; it is required to make an ...
Side 36
I. Book I. each of these the angle BGH ; therefore the angles EGB , BGH are equal to the angles BGH , GHD ; but EGB , BGH are e- qual to two right ... O draw a ftraight line through a given point paral- lel to a given straight line .
I. Book I. each of these the angle BGH ; therefore the angles EGB , BGH are equal to the angles BGH , GHD ; but EGB , BGH are e- qual to two right ... O draw a ftraight line through a given point paral- lel to a given straight line .
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The First Six Books: Together with the Eleventh and Twelfth Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.