The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Σελίδα 467
Bisect AB in D ; and to AD , DB , which are equal , let DC be added ; then AC will
be equal to BD and DC together ; that is , to BC and twice DC ; consequently
twice DC is the difference , and DC half that difference ; but AC the greater is
equal ...
Bisect AB in D ; and to AD , DB , which are equal , let DC be added ; then AC will
be equal to BD and DC together ; that is , to BC and twice DC ; consequently
twice DC is the difference , and DC half that difference ; but AC the greater is
equal ...
Σελίδα 469
that is , ( since ED is the sum of the sides BA , AC , and FD their difference , ( 3. of
this , ) ) as the tangent of half the sum of the angles B , C , at the base to the
tangent of half their difference . Therefore , in any plane triangle , & c . Q. E. D.
PROP ...
that is , ( since ED is the sum of the sides BA , AC , and FD their difference , ( 3. of
this , ) ) as the tangent of half the sum of the angles B , C , at the base to the
tangent of half their difference . Therefore , in any plane triangle , & c . Q. E. D.
PROP ...
Σελίδα 472
12. 13 . In a plane triangle , the base is to the sum of the sides as the difference of
the sides is to the sum or difference of the segments of the base made by the
perpendicular upon it from the vertex , according as the square of the greater side
...
12. 13 . In a plane triangle , the base is to the sum of the sides as the difference of
the sides is to the sum or difference of the segments of the base made by the
perpendicular upon it from the vertex , according as the square of the greater side
...
Σελίδα 478
Whence OP - FM = OP - ON = NP = EL the sine of EB the difference of the arches
. Q. E. I. COR . Since the differences of the arches BE , BD , BF are equal , the
arch BD is an arithmetical mean between the arches BE and BF ; or , the greater
of ...
Whence OP - FM = OP - ON = NP = EL the sine of EB the difference of the arches
. Q. E. I. COR . Since the differences of the arches BE , BD , BF are equal , the
arch BD is an arithmetical mean between the arches BE and BF ; or , the greater
of ...
Σελίδα 505
But A B the arch ADB is the semi - circumference of the circle , therefore the arch
CE is a quadrant ; consequently DE ( which is the difference between the arch
CD and the quadrant CE ) is the complement of CD . Cor . Hence the sine and ...
But A B the arch ADB is the semi - circumference of the circle , therefore the arch
CE is a quadrant ; consequently DE ( which is the difference between the arch
CD and the quadrant CE ) is the complement of CD . Cor . Hence the sine and ...
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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 |