The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Del 1John Weale, 1853 - 136 sider |
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Side xii
... four different propositions may be framed , which , for con- venience , are distinguished by the four vowels , A , E , I , and 0 ; the following table enumerates them , and gives an example of each : - A Universal Affirmative E ...
... four different propositions may be framed , which , for con- venience , are distinguished by the four vowels , A , E , I , and 0 ; the following table enumerates them , and gives an example of each : - A Universal Affirmative E ...
Side xvi
... four different kinds of propositions , it may be shown by the laws of combination that 64 different syllogisms ( or Moods , as they are termed ) , may be formed with the same terms ; thus , the major pre- miss may be either A , E , I ...
... four different kinds of propositions , it may be shown by the laws of combination that 64 different syllogisms ( or Moods , as they are termed ) , may be formed with the same terms ; thus , the major pre- miss may be either A , E , I ...
Side xvii
... four in all ; and of these five are rejected as useless , because they give only a particular con- clusion when a universal one might have been drawn from the premises . In order to impress upon the memory the nineteen allowable moods ...
... four in all ; and of these five are rejected as useless , because they give only a particular con- clusion when a universal one might have been drawn from the premises . In order to impress upon the memory the nineteen allowable moods ...
Side 3
... four right angles or an entire revolution . We have only to conceive the line as moving at a uniform rate , so that the magnitude of the angle may be estimated by the length of time that it has been in motion , to see that , if the time ...
... four right angles or an entire revolution . We have only to conceive the line as moving at a uniform rate , so that the magnitude of the angle may be estimated by the length of time that it has been in motion , to see that , if the time ...
Side 5
... four straight lines . SCHOLIUM . A straight line drawn from any two opposite angles of a quadrilateral figure is termed a diagonal . 26. A PARALLELOGRAM is a quadrilateral figure whose opposite sides are parallel . SCHOLIUM . If a ...
... four straight lines . SCHOLIUM . A straight line drawn from any two opposite angles of a quadrilateral figure is termed a diagonal . 26. A PARALLELOGRAM is a quadrilateral figure whose opposite sides are parallel . SCHOLIUM . If a ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 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.
Side 13 - The difference between any two sides of a triangle is less than the third side.
Side 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.
Side 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.
Side 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
Side 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Side 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...