Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |
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Σελίδα 105
To incribe an equilateral and equiangular hexagon in a given circle . Let
ABCDEF be the given circle ; it is required to inscribe an equilateral and
equiangular hexagon in it . Find the centre G of the circle ABCDEF , and draw the
diameter AGD ...
To incribe an equilateral and equiangular hexagon in a given circle . Let
ABCDEF be the given circle ; it is required to inscribe an equilateral and
equiangular hexagon in it . Find the centre G of the circle ABCDEF , and draw the
diameter AGD ...
Σελίδα 106
AFE is equal to FED : in the same manner it may be demonstrated , that the other
angles of the hexagon ABCDEF are each of them equal to the angle AFE or FED
; therefore the hexagon is equiangular ; it is also equilateral , as was shown ...
AFE is equal to FED : in the same manner it may be demonstrated , that the other
angles of the hexagon ABCDEF are each of them equal to the angle AFE or FED
; therefore the hexagon is equiangular ; it is also equilateral , as was shown ...
Σελίδα 130
and the triangle ABC is therefore equiangular to the triangle GEF ; and
consequently they B C G have their sides opposite to the equal angles
proportionals ( 4. 6. ) . Wherefore , ĀB : BC :: GÈ : EF ; but by supposition , AB :
BC :: DE : EF ...
and the triangle ABC is therefore equiangular to the triangle GEF ; and
consequently they B C G have their sides opposite to the equal angles
proportionals ( 4. 6. ) . Wherefore , ĀB : BC :: GÈ : EF ; but by supposition , AB :
BC :: DE : EF ...
Σελίδα 139
G Nord K 1 whole CFE : for the same reason , the angle ABH is equal to the
angle CDE ; also the angle at A is equal to the angle at C , and the angle GHB to
FED : Therefore the rectilineal figure ABHG is equiangular to CDEF : but likewise
...
G Nord K 1 whole CFE : for the same reason , the angle ABH is equal to the
angle CDE ; also the angle at A is equal to the angle at C , and the angle GHB to
FED : Therefore the rectilineal figure ABHG is equiangular to CDEF : but likewise
...
Σελίδα 157
and the angle BAC is either the same with DAF , or vertical to it ; therefore the
triangles ABC , ADF are equiangular , and BA : AC :: AD : AF ( 4.6 . ) ; therefore
also the rectangle BA.AF , contained by the extremes , is equal to the rectangle
AC.
and the angle BAC is either the same with DAF , or vertical to it ; therefore the
triangles ABC , ADF are equiangular , and BA : AC :: AD : AF ( 4.6 . ) ; therefore
also the rectangle BA.AF , contained by the extremes , is equal to the rectangle
AC.
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 62 - 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 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 130 - 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 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - 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.
Σελίδα 55 - 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.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |
| Συγγραφέας | John Playfair |
| Επιμελητής | John Playfair |
| Μεταφράστηκε από | John Playfair |
| Έκδοση | 5 |
| Εκδότης | G. Long, 1819 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |