The First Six Books: Together with the Eleventh and Twelfth |
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Page 120
Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is ufually expreffed by faying , the first is to the second , as the third to the fourth . ' VII .
Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is ufually expreffed by faying , the first is to the second , as the third to the fourth . ' VII .
Page 121
In proportionals , the antecedent terms are called homologous to one another , as alfo the confequents to one another . Geometers make use of the following technical words to fig- nify certain ways of changing either the order or magni- ...
In proportionals , the antecedent terms are called homologous to one another , as alfo the confequents to one another . Geometers make use of the following technical words to fig- nify certain ways of changing either the order or magni- ...
Page 122
Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , fo that they are proportionals when taken two and two of each rank , and it is ...
Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , fo that they are proportionals when taken two and two of each rank , and it is ...
Page 129
... or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROP . B. THEOR . IF four magnitudes are proportionals , they are propor- see N. tionals ...
... or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROP . B. THEOR . IF four magnitudes are proportionals , they are propor- see N. tionals ...
Page 136
... be proportionals , as one of the antecedents is to its confequent , fo fhall all the antecedents taken together be to all the confequents . Let any number of magnitudes A , B , C , D , E , F , be propor tionals ; that is , as A is ...
... be proportionals , as one of the antecedents is to its confequent , fo fhall all the antecedents taken together be to all the confequents . Let any number of magnitudes A , B , C , D , E , F , be propor tionals ; that is , as A is ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.