Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer1879 |
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Page 9
... is required ; see , for instance , note to Prop . 15 . The beginner will understand these distinctions and divi- sions more B 3 Part I. - Euclid , Books I. II . 9 being continually produced, shall at length meet on that ...
... is required ; see , for instance , note to Prop . 15 . The beginner will understand these distinctions and divi- sions more B 3 Part I. - Euclid , Books I. II . 9 being continually produced, shall at length meet on that ...
Page 14
... prop . 1 ) ; the learner will find that throughout Euclid the successive propositions are linked to and depend upon the preceding ones , as the successive links of a chain hang one from another . When the given point is neither in the ...
... prop . 1 ) ; the learner will find that throughout Euclid the successive propositions are linked to and depend upon the preceding ones , as the successive links of a chain hang one from another . When the given point is neither in the ...
Page 19
... prop . 4 , ( 2 ) As BCF , BCG are also proved equal by prop . 4 , ( 3 ) ≤s ABC , ACB are proved equal by ax . 3 . A corollary ( cor . ) is an inference which at once follows from the demonstration of a proposition : in fact , it is a ...
... prop . 4 , ( 2 ) As BCF , BCG are also proved equal by prop . 4 , ( 3 ) ≤s ABC , ACB are proved equal by ax . 3 . A corollary ( cor . ) is an inference which at once follows from the demonstration of a proposition : in fact , it is a ...
Page 20
... prop . 5. One prop . is said to be the converse of another when the conclusion of each is the hypothesis of the other . In prop . 5 20 Pupil - Teacher's Course of Mathematics .
... prop . 5. One prop . is said to be the converse of another when the conclusion of each is the hypothesis of the other . In prop . 5 20 Pupil - Teacher's Course of Mathematics .
Page 21
... prop . 6 the hypothesis is the equality of the base angles , and the conclusion the equality of the sides . Converse propositions are not univer- sally true : an example of this will be given in the note to prop . 8 . This is the first ...
... prop . 6 the hypothesis is the equality of the base angles , and the conclusion the equality of the sides . Converse propositions are not univer- sally true : an example of this will be given in the note to prop . 8 . This is the first ...
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Common terms and phrases
ABCD algebraical angle contained angle equal base BC beginner centre coincide compl Constr contains a units demonstration describe sq diagonal diameter double of sq double sq draw equal angles equal sides equilat equilateral triangle Euclid exterior angle four rt geometrical given line given point given rectilineal given st given straight line gnomon CMG greater half a rt hypotenuse isosceles triangle join less Let AB contain Let ABC line drawn meet opposite angles opposite sides parallel parallelogram PROBLEM produced prop proved quadrilateral rectangle contained rectil right angles right-angled triangle sides equal square THEOREM triangle ABC twice rect unequal vertex
Popular passages
Page 48 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 32 - 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.
Page 2 - 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. 17. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 109 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.
Page 1 - ... angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which \ is less than a right angle. 13. A term or boundary is the extremity of any thing.
Page 6 - Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Page 77 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 3 - An equilateral triangle is that which has three equal sides : 25. An isosceles triangle is that which has two sides equal : 26. A scalene triangle is that which has three unequal sides : 27.
Page 1 - 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.
Page 84 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.