The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Μέρος 1John Weale, 1853 - 136 σελίδες |
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Σελίδα 2
... lines . By way of explanation , let us borrow an illustration from the hands of a clock , and regard the angle formed by their center lines . Now at twelve o'clock , as the hands coincide , no angle is 2 ELEMENTS OF GEOMETRY .
... lines . By way of explanation , let us borrow an illustration from the hands of a clock , and regard the angle formed by their center lines . Now at twelve o'clock , as the hands coincide , no angle is 2 ELEMENTS OF GEOMETRY .
Σελίδα 3
... coincide , no angle is formed by them ; but from that moment they cease to coincide , and the magnitude of the angle becomes every instant greater as the minute hand moves away from the other . Now at any definite portion of time , such ...
... coincide , no angle is formed by them ; but from that moment they cease to coincide , and the magnitude of the angle becomes every instant greater as the minute hand moves away from the other . Now at any definite portion of time , such ...
Σελίδα 7
... coincide in two points , they coincide when produced . " 11. All right angles are equal to one another . SCHOLIUM . Angles being a species of magnitude , this axiom is a parti- cular case of the 8th . 12. Through the same point two ...
... coincide in two points , they coincide when produced . " 11. All right angles are equal to one another . SCHOLIUM . Angles being a species of magnitude , this axiom is a parti- cular case of the 8th . 12. Through the same point two ...
Σελίδα 11
... coincide with the points E and F , the base BC must coincide with the base EF , and be equal to it ( c ) ; for otherwise two straight lines would enclose a space ( a ) . [ 2. ] And as the sides which form the angles B and C coincide ...
... coincide with the points E and F , the base BC must coincide with the base EF , and be equal to it ( c ) ; for otherwise two straight lines would enclose a space ( a ) . [ 2. ] And as the sides which form the angles B and C coincide ...
Σελίδα 13
... coincide with the point B , the point B with C , the angle ACB with the angle ABC , and the angle BCG with the angle CBF ; and therefore [ 1 ] the angle ACB will be equal to the angle ABC ( b ) , and [ 2 ] the angle BCG equal to the ...
... coincide with the point B , the point B with C , the angle ACB with the angle ABC , and the angle BCG with the angle CBF ; and therefore [ 1 ] the angle ACB will be equal to the angle ABC ( b ) , and [ 2 ] the angle BCG equal to the ...
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...