The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
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Αποτελέσματα 1 - 5 από τα 27.
Σελίδα 8
DL is equal to DG ; and DA , DB , parts of them are equal ( Construction ) ;
therefore , ( Ax . 3 . ) 3 . ... But it has been shown that BC is equal to BG ;
wherefore AL and BC are each of them equal to BG ; and things that are equal to
the same are ...
DL is equal to DG ; and DA , DB , parts of them are equal ( Construction ) ;
therefore , ( Ax . 3 . ) 3 . ... But it has been shown that BC is equal to BG ;
wherefore AL and BC are each of them equal to BG ; and things that are equal to
the same are ...
Σελίδα 10
In BD take any point F , and from AE , the greater , cut off AG equal ( I . 3 . ) to AF ,
the less , and join FC , GB . Because AF is equal ( Constr . ) to AG , and AB (
Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to ...
In BD take any point F , and from AE , the greater , cut off AG equal ( I . 3 . ) to AF ,
the less , and join FC , GB . Because AF is equal ( Constr . ) to AG , and AB (
Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to ...
Σελίδα 13
Let ABC , DEF , be two triangles having the two sides AB , AC , equal to the two
sides DE , DF , each to each , viz . AB to DE , and AC ... T ' he two sides DA , AF ,
are equal to the two sides EA , AF , each to each ; and ( Constr . ) 2 . The base DF
...
Let ABC , DEF , be two triangles having the two sides AB , AC , equal to the two
sides DE , DF , each to each , viz . AB to DE , and AC ... T ' he two sides DA , AF ,
are equal to the two sides EA , AF , each to each ; and ( Constr . ) 2 . The base DF
...
Σελίδα 14
and ( Constr . ) 2 . The base DF is equal to the base EF ; therefore ( I . 8 . ) 3 . The
angle DAF is equal to the angle EAF ; wherefore 4 . The angle BAC is bisected by
the straight line AF . Which was to be done . PROP . X . - PROBLEM . To bisect ...
and ( Constr . ) 2 . The base DF is equal to the base EF ; therefore ( I . 8 . ) 3 . The
angle DAF is equal to the angle EAF ; wherefore 4 . The angle BAC is bisected by
the straight line AF . Which was to be done . PROP . X . - PROBLEM . To bisect ...
Σελίδα 15
The two sides DC , CF , are equal to the two EC , CF , each to each ; and ( Constr
. ) 2 . The base DF is equal to the base EF ; therefore ( I . 8 . ) 3 . The angle DCF is
equal to the angle ECF ; and they are adjacent angles . But when the adjacent ...
The two sides DC , CF , are equal to the two EC , CF , each to each ; and ( Constr
. ) 2 . The base DF is equal to the base EF ; therefore ( I . 8 . ) 3 . The angle DCF is
equal to the angle ECF ; and they are adjacent angles . But when the adjacent ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal angle ABC angle ACB angle BAC angle BCD angle equal base base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles equal Constr exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown sides square of AC straight line AC touches the circle triangle ABC twice the rectangle wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 26 - 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...
Σελίδα 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 32 - 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 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Σελίδα 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - AB; but things which are equal to the same are equal to one another...
Σελίδα 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Σελίδα 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Σελίδα 41 - 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.
Σελίδα 52 - 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...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
| Συγγραφέας | Euclides |
| Επιμελητής | Samuel A Good |
| Εκδόθηκε | 1853 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 7 Σεπτ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |