The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 48
... square upon a given straight line . Let AB be the given ftraight line ; it is required to defcribe a fquare upon AB . E From the point A draw AC at right angles to AB ; and make AD equal to AB , and through the point D draw DE parallel ...
... square upon a given straight line . Let AB be the given ftraight line ; it is required to defcribe a fquare upon AB . E From the point A draw AC at right angles to AB ; and make AD equal to AB , and through the point D draw DE parallel ...
Σελίδα 50
... AC ; therefore the squares of DA , AC , are equal to the squares of BA , AC : But the fquare of DC is equal A to the fquares of DA , AC , because DAC is a right angle ; and the square of BC , by hypothefis , is equal to the fquares of BA , ...
... AC ; therefore the squares of DA , AC , are equal to the squares of BA , AC : But the fquare of DC is equal A to the fquares of DA , AC , because DAC is a right angle ; and the square of BC , by hypothefis , is equal to the fquares of BA , ...
Σελίδα 53
... AC ; for it is con- Book II . tained by DA , AC , of which AD is equal to AB ; and CE is contained by AB , BC , for ... square of the forefaid part . Let the straight line AB be divided into any two parts in the point C ; the rectangle ...
... AC ; for it is con- Book II . tained by DA , AC , of which AD is equal to AB ; and CE is contained by AB , BC , for ... square of the forefaid part . Let the straight line AB be divided into any two parts in the point C ; the rectangle ...
Σελίδα 56
... square of CB , is equal to the fquare of CD . Upon CD defcribe the fquare CEFD , join DE , and through B draw BHG ... AC A is equal to CB , the rectangle c 36. I. AL is equal to CH ; but d 43. I. CH is equal to HF ; there- fore alfo AL ...
... square of CB , is equal to the fquare of CD . Upon CD defcribe the fquare CEFD , join DE , and through B draw BHG ... AC A is equal to CB , the rectangle c 36. I. AL is equal to CH ; but d 43. I. CH is equal to HF ; there- fore alfo AL ...
Σελίδα 60
... square of AF , because the angle ADF is a right angle ; therefore the fquares of AD , DF are double of the fquares of AC , CD : And DF is equal to DB ; therefore the iquares of AD , DB are double of the fquares of AC , CD . If therefore ...
... square of AF , because the angle ADF is a right angle ; therefore the fquares of AD , DF are double of the fquares of AC , CD : And DF is equal to DB ; therefore the iquares of AD , DB are double of the fquares of AC , CD . If therefore ...
Άλλες εκδόσεις - Προβολή όλων
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.