The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Μέρος 1John Weale, 1853 - 136 σελίδες |
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Σελίδα xv
... remaining unaltered ) so that its converse may be only a particular affirmative proposition ; for instance , the universal affirmative proposition , " Every X is Y , " may be illatively converted ; per accidens , into the particular ...
... remaining unaltered ) so that its converse may be only a particular affirmative proposition ; for instance , the universal affirmative proposition , " Every X is Y , " may be illatively converted ; per accidens , into the particular ...
Σελίδα 13
... remaining angles must be equal , BCF to CBG ( f ) ; and if these equal angles be taken from the equal angles ACF and ABG , the remaining angles , ACB and ABC , will be equal ( g ) , which are the angles at the base of the given triangle ...
... remaining angles must be equal , BCF to CBG ( f ) ; and if these equal angles be taken from the equal angles ACF and ABG , the remaining angles , ACB and ABC , will be equal ( g ) , which are the angles at the base of the given triangle ...
Σελίδα 19
... remaining angles ABE and ABD shall be equal ( d ) a part to the whole , which is absurd ; therefore ( a ) I. 13 . ( b ) Hypoth . ( c ) Ax . 1 . ( d ) Ax . 3 . BE is not the continuation of CB . And in ELEMENTS OF GEOMETRY . 19.
... remaining angles ABE and ABD shall be equal ( d ) a part to the whole , which is absurd ; therefore ( a ) I. 13 . ( b ) Hypoth . ( c ) Ax . 1 . ( d ) Ax . 3 . BE is not the continuation of CB . And in ELEMENTS OF GEOMETRY . 19.
Σελίδα 20
... remaining angles CEA and DEB shall be equal ( c ) . And in like manner it can be proved that the angles CEB and AED are equal . ( a ) I. 13 . ( b ) Ax . 1 . ( c ) Ax . 3 . SCHOLIA . 1. The second and third corollaries to proposition ...
... remaining angles CEA and DEB shall be equal ( c ) . And in like manner it can be proved that the angles CEB and AED are equal . ( a ) I. 13 . ( b ) Ax . 1 . ( c ) Ax . 3 . SCHOLIA . 1. The second and third corollaries to proposition ...
Σελίδα 28
... remaining angles and sides shall be respectively equal to one another . AA B DEMONSTRATION . [ 1. ] Let the equal sides be BC and EF , the sides adjacent to the equal angles , then the side BA is equal to ED . For if it be possible ...
... remaining angles and sides shall be respectively equal to one another . AA B DEMONSTRATION . [ 1. ] Let the equal sides be BC and EF , the sides adjacent to the equal angles , then the side BA is equal to ED . For if it be possible ...
Άλλες εκδόσεις - Προβολή όλων
The elements of Euclid, [books I.-VI. XI. XII.] with many additional ... Eucleides Πλήρης προβολή - 1853 |
The Elements of Euclid with Many Additional Propositions and Explanatory Notes Henry Law,Eucleides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AC and CB AC is equal angle ABC angle BCD angle equal area to double area to twice bisect chord circle ABC circumference Constr CONSTRUCTION COROLLARY DB is equal DEMONSTRATION diagonal divided double the rectangle draw equal angles equal in area equal to AC equilateral Euclid external angle Find the center finite straight line Geometry given angle given line greater Hypoth HYPOTHESES intersect join less line BC lines be drawn magnitude major premiss opposite sides parallel parallelogram perpendicular predicate premises produced proposition quadratic equation reductio ad absurdum right angles SCHOLIA SCHOLIUM second power segment sides AC square on AC square on half squares on AB syllogism termed THEOREM THEOREM.-If triangle ABC twice the rectangle twice the square vertex whole line
Δημοφιλή αποσπάσματα
Σελίδα 24 - 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 114 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Σελίδα xiv - 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 : 16. And this point is called the centre of the circle.
Σελίδα 13 - The difference between any two sides of a triangle is less than the third side.
Σελίδα 111 - AFC. (in. 21.) Hence in the triangles ADE, AFC, there are two angles in the one respectively equal to two angles in the other, consequently, the third angle CAF is equal to the third angle DAB ; therefore the arc DB is equal to the arc CF, (in.
Σελίδα 89 - ... the centre of the circle shall be in that line. Let the straight line DE touch the circle ABC in C, and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA.
Σελίδα 70 - EQUAL circles are those of which the diameters are equal, or from the centres of which the straight lines to the circumferences are equal. ' This is not a definition, but a theorem, the truth of ' which is evident; for, if the circles be applied to one ' another, so that their centres coincide, the circles ' must likewise coincide, since the straight lines from
Σελίδα 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Σελίδα 22 - 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...