The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Σελίδα 261
peds of the same altitude with the cone , which are also prisms , Book XII . the
prism upon the square ABCD will be the half of that which is upon the square
described about the circle ; for they are to one another as their bases e ; as H e
32.
peds of the same altitude with the cone , which are also prisms , Book XII . the
prism upon the square ABCD will be the half of that which is upon the square
described about the circle ; for they are to one another as their bases e ; as H e
32.
Σελίδα 262
THEOR . See N. Cones and cylinders of the same altitude , are to one another as
their bases . ... If it be not so , let the circle ABCD be to the circle EFGH , as the
cone AL to some solid either less than the cone EN , or greater than it . First , Let
it ...
THEOR . See N. Cones and cylinders of the same altitude , are to one another as
their bases . ... If it be not so , let the circle ABCD be to the circle EFGH , as the
cone AL to some solid either less than the cone EN , or greater than it . First , Let
it ...
Σελίδα 264
N : But the cone AL is greater than the pyramid contained in it ; therefore the solid
X is greater than the pyramid in e 14. 5. the cone EN . But it is less , as was
shown , which is absurd : L D V N H S R A СЕ G K M T P B F X I Z Therefore the
circle ...
N : But the cone AL is greater than the pyramid contained in it ; therefore the solid
X is greater than the pyramid in e 14. 5. the cone EN . But it is less , as was
shown , which is absurd : L D V N H S R A СЕ G K M T P B F X I Z Therefore the
circle ...
Σελίδα 265
cyis to the circle EFGH , as the cone AL to the cone EN : Book XII . But as the
cone is to the cone , sob is the cylinder to the linder , because the cylinders are
triple the cones , each to b 15. 5 . each . Therefore , as the circle ABCD to the
circle ...
cyis to the circle EFGH , as the cone AL to the cone EN : Book XII . But as the
cone is to the cone , sob is the cylinder to the linder , because the cylinders are
triple the cones , each to b 15. 5 . each . Therefore , as the circle ABCD to the
circle ...
Σελίδα 268
But as the solid Z is to the cone ABCDL , so is the cone EFGHN to some solid ,
which must be less a than the cone a 14. 5 . ABCDL , because the solid Z is
greater than the cone EFGHN : Therefore the cone EFGIN has to a solid which is
less ...
But as the solid Z is to the cone ABCDL , so is the cone EFGHN to some solid ,
which must be less a than the cone a 14. 5 . ABCDL , because the solid Z is
greater than the cone EFGHN : Therefore the cone EFGIN has to a solid which is
less ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter difference divided double draw drawn equal equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Σελίδα 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Σελίδα 153 - 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 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Σελίδα 28 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Σελίδα 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Συγγραφέας | Euclid |
| Επιμελητής | Robert Simson |
| Εκδότης | Bell & Bradfute, 1835 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 6 Μάιος 2008 |
| Μέγεθος | 513 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |