Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer1879 |
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Side 64
... square of which the given line shall be a diagonal . 2. The difference of the angles at the base of any triangle is double the angle contained by two lines drawn from the vertex , one bisecting the vertical angle , the other ...
... square of which the given line shall be a diagonal . 2. The difference of the angles at the base of any triangle is double the angle contained by two lines drawn from the vertex , one bisecting the vertical angle , the other ...
Side 87
... double of △ ABD , ... they are on the same base BD and between the same || s BD , AL ; ( i . 41 ) also the sq . GB is double of △ FBC , they are on the same base FB and between the same || s FB , GC . ( i . 41 ) But the doubles of ...
... double of △ ABD , ... they are on the same base BD and between the same || s BD , AL ; ( i . 41 ) also the sq . GB is double of △ FBC , they are on the same base FB and between the same || s FB , GC . ( i . 41 ) But the doubles of ...
Side 88
... squares on these lines are together double the square on the radius . 4. From the middle point of a side of a right - angled triangle a perpendicular is drawn to the hypotenuse : show that the difference of the squares on the segments ...
... squares on these lines are together double the square on the radius . 4. From the middle point of a side of a right - angled triangle a perpendicular is drawn to the hypotenuse : show that the difference of the squares on the segments ...
Side 108
... squares on the two unequal parts are together double of the square on half the line , and of the square on the line between the points of section . Let the st . line AB be divided into two equal parts at C , and into two unequal parts ...
... squares on the two unequal parts are together double of the square on half the line , and of the square on the line between the points of section . Let the st . line AB be divided into two equal parts at C , and into two unequal parts ...
Side 109
... sq . on CE , .. sqs . on AC , CE are together double of sq . on AC ; but sq . on AE is = sqs . on AC , CE ; Again , .. sq . on AE is double of sq . on AC . ( i . 47 ) EG = GF , .. sq . on EG = sq . on GF , .. sqs . on EG , GF are ...
... sq . on CE , .. sqs . on AC , CE are together double of sq . on AC ; but sq . on AE is = sqs . on AC , CE ; Again , .. sq . on AE is double of sq . on AC . ( i . 47 ) EG = GF , .. sq . on EG = sq . on GF , .. sqs . on EG , GF are ...
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Euclid, Books I. & II., with Notes, Examples, and Explanations, by a Late ... Euclides Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.