The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Parte1John Weale, 1853 - 136 páginas |
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Página xi
... third division of propositions is according to their quantity into universal and particular . A proposition is said to be univer- sal when the predicate refers to the whole of the subject , as , " Every equiangular triangle is ...
... third division of propositions is according to their quantity into universal and particular . A proposition is said to be univer- sal when the predicate refers to the whole of the subject , as , " Every equiangular triangle is ...
Página xv
... third figure the middle term is the subject in both pre- mises , as in the syllogism- * In all these examples the middle term is enclosed in parentheses . b 2 xvi INTRODUCTION . [ Major Premiss ] Every ( square INTRODUCTION . XV.
... third figure the middle term is the subject in both pre- mises , as in the syllogism- * In all these examples the middle term is enclosed in parentheses . b 2 xvi INTRODUCTION . [ Major Premiss ] Every ( square INTRODUCTION . XV.
Página xvi
... third , those two terms disagree with each other . 3. If neither of two terms agree with the third , those two terms may either agree or disagree with each other . From these axioms six general rules are deduced ; we shall here only ...
... third , those two terms disagree with each other . 3. If neither of two terms agree with the third , those two terms may either agree or disagree with each other . From these axioms six general rules are deduced ; we shall here only ...
Página xvii
... third figure the special rules are— 1. The minor premiss must be affirmative . 2. The conclusion must be particular . XVI In the fourth figure there are three special rules ; namely → 1. If the major premiss be affirmative , the minor ...
... third figure the special rules are— 1. The minor premiss must be affirmative . 2. The conclusion must be particular . XVI In the fourth figure there are three special rules ; namely → 1. If the major premiss be affirmative , the minor ...
Página 5
... third side opposite to the right angle is termed the hypotenuse ; and in any triangle any side is said to subtend the angle opposite to it ; thus the hypotenuse subtends the right angle . 23. An OBTUSE - ANGLED TRIANGLE is a triangle ...
... third side opposite to the right angle is termed the hypotenuse ; and in any triangle any side is said to subtend the angle opposite to it ; thus the hypotenuse subtends the right angle . 23. An OBTUSE - ANGLED TRIANGLE is a triangle ...
Otras ediciones - Ver todas
The elements of Euclid, [books I.-VI. XI. XII.] with many additional ... Eucleides Vista completa - 1853 |
The Elements of Euclid with Many Additional Propositions and Explanatory Notes Henry Law,Eucleides Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 13 - The difference between any two sides of a triangle is less than the third side.
Página 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.
Página 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.
Página 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
Página 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Página 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...