Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer1879 |
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Σελίδα 30
... common segment . [ Avoid a very common improper application of prop . 8 . After saying , and the base DF = the base EF , ' boys often go on ... the As DCF , FCE are equal in all respects , -by i . 8 , ' & c . Now Euclid does not prove ...
... common segment . [ Avoid a very common improper application of prop . 8 . After saying , and the base DF = the base EF , ' boys often go on ... the As DCF , FCE are equal in all respects , -by i . 8 , ' & c . Now Euclid does not prove ...
Σελίδα 31
... common to As FHC , GHC ; the two sides FH , HC each to each ; and base CF = base CG ; GH , HC , ( def . 15 ) .. / FHC = ≤ GHC ( i . 8 ) , and these are adj . s . But , when a st . line standing on another st . line makes the adj . Zs ...
... common to As FHC , GHC ; the two sides FH , HC each to each ; and base CF = base CG ; GH , HC , ( def . 15 ) .. / FHC = ≤ GHC ( i . 8 ) , and these are adj . s . But , when a st . line standing on another st . line makes the adj . Zs ...
Σελίδα 35
... common △ AED , and remaining CEA = remaining DEB . ( ax . 3 ) In the same way it may be demonstrated that CEB = AED . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that if two st . lines cut ...
... common △ AED , and remaining CEA = remaining DEB . ( ax . 3 ) In the same way it may be demonstrated that CEB = AED . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that if two st . lines cut ...
Σελίδα 37
... ACD may be proved greater than △ ABC - a common mistake . ] Any two exterior angles of a triangle are together greater than two right angles . PROPOSITION XVII . THEOREM . Any two angles of a Part I. - Euclid , Books I. II . 37.
... ACD may be proved greater than △ ABC - a common mistake . ] Any two exterior angles of a triangle are together greater than two right angles . PROPOSITION XVII . THEOREM . Any two angles of a Part I. - Euclid , Books I. II . 37.
Σελίδα 52
... , ( 2 ) when they are opposite the equal angles , are quite independent . It is a very common error to prove the equality of two other sides , each to each , and then to stop with the 52 Pupil - Teacher's Course of Mathematics .
... , ( 2 ) when they are opposite the equal angles , are quite independent . It is a very common error to prove the equality of two other sides , each to each , and then to stop with the 52 Pupil - Teacher's Course of Mathematics .
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Euclid, Books I. & II., with Notes, Examples, and Explanations, by a Late ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.