First principles of Euclid: an introduction to the study of the first book of Euclid's Elements1880 |
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Σελίδα 5
... conclusion ( a conclusion I find arrived at by many thoughtful teachers ) that the reason is threefold . In the first place , when Euclid wrote his Elements , more than two thousand years ago , he little thought they would form a text ...
... conclusion ( a conclusion I find arrived at by many thoughtful teachers ) that the reason is threefold . In the first place , when Euclid wrote his Elements , more than two thousand years ago , he little thought they would form a text ...
Σελίδα 6
... conclusion follows from the premisses . In the third place , the various editions of Euclid do not help the learner to apply any power of geome- trical reasoning he may attain . True , they generally contain deductions to be worked out ...
... conclusion follows from the premisses . In the third place , the various editions of Euclid do not help the learner to apply any power of geome- trical reasoning he may attain . True , they generally contain deductions to be worked out ...
Σελίδα 10
... Conclusion . Now suppose we put the letters X , Y , and Z , for the words boy , head , and John , our syllogism will read thus : Every X has Y. Z is X. Therefore Z has Y. This is a sort of skeleton syllogism , having the general form in ...
... Conclusion . Now suppose we put the letters X , Y , and Z , for the words boy , head , and John , our syllogism will read thus : Every X has Y. Z is X. Therefore Z has Y. This is a sort of skeleton syllogism , having the general form in ...
Σελίδα 11
... conclusion given . But , whether expressed or understood , two premisses are absolutely necessary to form a conclusion . To distinguish one premiss from the other , the first is called the major premiss , and the second the minor ...
... conclusion given . But , whether expressed or understood , two premisses are absolutely necessary to form a conclusion . To distinguish one premiss from the other , the first is called the major premiss , and the second the minor ...
Σελίδα 12
... Conclusion ... AB and AC are equal . B Major Premiss . A Minor Premiss . AB and CD C are parallel lines . B D Conclusion ... A B and CD if produced will never meet . Major Premiss . Minor Premiss . The line CD stand- 12 First Principles ...
... Conclusion ... AB and AC are equal . B Major Premiss . A Minor Premiss . AB and CD C are parallel lines . B D Conclusion ... A B and CD if produced will never meet . Major Premiss . Minor Premiss . The line CD stand- 12 First Principles ...
Συχνά εμφανιζόμενοι όροι και φράσεις
1st conclusion 2nd Syllogism A B equal ABC is equal adjacent angles alternate angle angle A CD angle ABC angle B A C angle BAC angle contained angle DFE angle EDF angle GHD angles BGH angles equal Axiom 2a Axiom 9 base B C bisected CD is greater coincide Construction definition diameter enunciations of Euc equal angles equal to A B equal to angle equal to CD equal to side equilateral triangle EXERCISES.-I exterior angle figure given line given point given straight line greater than angle included angle interior opposite angle isosceles triangle Join Let us suppose line A B line CD major premiss parallel to CD parallelogram Particular Enunciation PROBLEM Euclid produced proposition prove that angle remaining angle Required right angles side A C sides equal square THEOREM Euclid triangle ABC
Δημοφιλή αποσπάσματα
Σελίδα 83 - 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 18 - 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.
Σελίδα 66 - If, from the ends of the 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. Let...
Σελίδα 34 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Σελίδα 94 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 88 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 104 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Σελίδα 140 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Σελίδα 51 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 132 - 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.