Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer1879 |
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Σελίδα 110
Euclides. gether with the square on their difference is double the squares on the two lines . 2. Divide a straight line into two parts so that the sum of their squares may be the least possible . 3. ABCD is a square and AC its diagonal ...
Euclides. gether with the square on their difference is double the squares on the two lines . 2. Divide a straight line into two parts so that the sum of their squares may be the least possible . 3. ABCD is a square and AC its diagonal ...
Σελίδα 111
... square on the whole line thus produced , and the square on the part of it produced , are together double of the square on half the line bisected , and of the square on the line made up of the half and the part produced . Let AB be ...
... square on the whole line thus produced , and the square on the part of it produced , are together double of the square on half the line bisected , and of the square on the line made up of the half and the part produced . Let AB be ...
Σελίδα 112
... sq . on CA ; .. sqs . on EC , CA are double of sq . on CA ; but sq . on EA = sqs . on EC , CA ; .. sq . on EA is double of sq . on CA. And but GF = EF , .. sq . on GF = sq . on EF , .. sqs . on GF , FE are double of sq . on EF ; sq . on ...
... sq . on CA ; .. sqs . on EC , CA are double of sq . on CA ; but sq . on EA = sqs . on EC , CA ; .. sq . on EA is double of sq . on CA. And but GF = EF , .. sq . on GF = sq . on EF , .. sqs . on GF , FE are double of sq . on EF ; sq . on ...
Σελίδα 113
... two parts so that the square on one part may be double the square on the other . ' Let the length of the line AB be a , suppose it be divided as required in D , and let DB = x . Then since sq . on AD = twice sq . on BD . * . ( a − x ) ...
... two parts so that the square on one part may be double the square on the other . ' Let the length of the line AB be a , suppose it be divided as required in D , and let DB = x . Then since sq . on AD = twice sq . on BD . * . ( a − x ) ...
Σελίδα 121
... squares on the sides of the triangle CDE is equal to two - thirds of the square on AB . 8. In any quadrilateral , the squares on the diagonals are together double of the sum of the squares on the two lines joining the bisections of the ...
... squares on the sides of the triangle CDE is equal to two - thirds of the square on AB . 8. In any quadrilateral , the squares on the diagonals are together double of the sum of the squares on the two lines joining the bisections of the ...
Άλλες εκδόσεις - Προβολή όλων
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.