The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |
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Αποτελέσματα 6 - 10 από τα 80.
Σελίδα 361
... mentioned . See the Note upon it , I PROP . III . F any given magnitudes be added together , their sum shall be given . Let any given magnitudes AB , BC be added together , their sum AC is given . 3 . Because AB is given , a magnitude equal ...
... mentioned . See the Note upon it , I PROP . III . F any given magnitudes be added together , their sum shall be given . Let any given magnitudes AB , BC be added together , their sum AC is given . 3 . Because AB is given , a magnitude equal ...
Σελίδα 362
... given ; and also BC together with CD , that is BD , is given . either AB is equal to CD , or one of them is greater than the other by a given magnitude . Because AC , BD are each of them given , they are either equal to one another , or ...
... given ; and also BC together with CD , that is BD , is given . either AB is equal to CD , or one of them is greater than the other by a given magnitude . Because AC , BD are each of them given , they are either equal to one another , or ...
Σελίδα 363
... given ; therefore the ratio of AC to CB is given . d . 17.5 . a . 2. Def . PROP . VII . 6 . I F two magnitudes which have a given ratio to one See N. another , be added together ; the whole magnitude shall have to each of them a given ...
... given ; therefore the ratio of AC to CB is given . d . 17.5 . a . 2. Def . PROP . VII . 6 . I F two magnitudes which have a given ratio to one See N. another , be added together ; the whole magnitude shall have to each of them a given ...
Σελίδα 364
... given magnitudes DE , EF . and because the gi- A ven magnitude AB has to BC the given ratio of DE to EF , if unto DE , EF , AB a fourth proportional can be found , this D CB F E d . 4. Dat . c . 2. Dat . which is BC is given ; and ...
... given magnitudes DE , EF . and because the gi- A ven magnitude AB has to BC the given ratio of DE to EF , if unto DE , EF , AB a fourth proportional can be found , this D CB F E d . 4. Dat . c . 2. Dat . which is BC is given ; and ...
Σελίδα 365
... magnitudes have given ratios to one another , and if they have given ratios , tho ' they be not the same , to some other magnitudes : these other magnitudes shall also have given ratios to one another . Let two or more magnitudes A , B , C ...
... magnitudes have given ratios to one another , and if they have given ratios , tho ' they be not the same , to some other magnitudes : these other magnitudes shall also have given ratios to one another . Let two or more magnitudes A , B , C ...
Συχνά εμφανιζόμενοι όροι και φράσεις
alſo altitude angle ABC angle BAC baſe BC BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonſtrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs likewife oppoſite parallel parallelepipeds parallelogram paſs perpendicular plane angles priſm PROP proportionals Propoſition pyramid rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhall be equal ſhewn ſide ſolid ſome ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.
Σελίδα 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.
Σελίδα 1 - 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, fourths, &c.
Σελίδα 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 163 - 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 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.