Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 77
... the Square of the whole line is equal to both the fquares of the parts , together with twice the rectangle contained under the parts . For let the right line A B be divided by the point c into any two parts : I fay , the fquare of A B ...
... the Square of the whole line is equal to both the fquares of the parts , together with twice the rectangle contained under the parts . For let the right line A B be divided by the point c into any two parts : I fay , the fquare of A B ...
Seite 79
... a square , viz . that of C B. For the fame reason HF is a fquare too , being equal to the square of AC : Therefore ... twice the rect- angle under the right lines A C , C B ; but alfo C K , HF , are equal to the fquares of A C , CB ...
... a square , viz . that of C B. For the fame reason HF is a fquare too , being equal to the square of AC : Therefore ... twice the rect- angle under the right lines A C , C B ; but alfo C K , HF , are equal to the fquares of A C , CB ...
Seite 82
... the Square of the whole line , together with that of one of the parts , will be equal to twice the rect- angle contained under the whole line and the faid part , together with the Square of the remaining parte . For let any right line ...
... the Square of the whole line , together with that of one of the parts , will be equal to twice the rect- angle contained under the whole line and the faid part , together with the Square of the remaining parte . For let any right line ...
Seite 83
... the square C F will be double to the rectangle AF . But twice the rectangle under AB , BC is double to AF : for [ by cor . 4. 2. ] B F is equal to B C. Therefore the gno- A H G K M N D mon KLM , and the fquare CF , are equal to twice ...
... the square C F will be double to the rectangle AF . But twice the rectangle under AB , BC is double to AF : for [ by cor . 4. 2. ] B F is equal to B C. Therefore the gno- A H G K M N D mon KLM , and the fquare CF , are equal to twice ...
Seite 89
... the square of the joined line , are equal to twice the fquare of one half the line , and the fquare of the line made of the half line , and the joined line taken as one line . Which was to be demonftrated . h This theorem may be ...
... the square of the joined line , are equal to twice the fquare of one half the line , and the fquare of the line made of the half line , and the joined line taken as one line . Which was to be demonftrated . h This theorem may be ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe whoſe baſe
Beliebte Passagen
Seite 247 - 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.
Seite 30 - 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...
Seite 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.
Seite 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Seite 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.
Seite 56 - 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.
Seite 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...
Seite 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 183 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...