Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer1879 |
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Resultat 1-5 av 9
Side 9
... follows the demonstration , showing the truth or falsehood of the theorem , or the possibility or im- possibility of the problem . The demonstration is said to be direct when the conclusion is obtained directly from the hypothesis . It ...
... follows the demonstration , showing the truth or falsehood of the theorem , or the possibility or im- possibility of the problem . The demonstration is said to be direct when the conclusion is obtained directly from the hypothesis . It ...
Side 19
... follows from the demonstration of a proposition : in fact , it is a simple ' rider ' ( see preface ) . The student should not leave it without seeing clearly why it so follows . ] 1. The middle point of the base of an isosceles tri ...
... follows from the demonstration of a proposition : in fact , it is a simple ' rider ' ( see preface ) . The student should not leave it without seeing clearly why it so follows . ] 1. The middle point of the base of an isosceles tri ...
Side 33
... follow . ] DB meets the straight line ABC in B ; BE , BF bisect the angles DBC , ABD . Show that FBE is a right angle . PROPOSITION XIV . THEOREM . If at a point in c 3 Part I. - Euclid , Books I. II . 33 . but CBE, EBD are two rt. △s...
... follow . ] DB meets the straight line ABC in B ; BE , BF bisect the angles DBC , ABD . Show that FBE is a right angle . PROPOSITION XIV . THEOREM . If at a point in c 3 Part I. - Euclid , Books I. II . 33 . but CBE, EBD are two rt. △s...
Side 40
... than one angle in the other , is demon- strated indirectly ; they thus follow , in this respect , the order of props . 5 and 6. ] PROPOSITION XX . THEOREM . Any two sides of a 40 Pupil - Teacher's Course of Mathematics .
... than one angle in the other , is demon- strated indirectly ; they thus follow , in this respect , the order of props . 5 and 6. ] PROPOSITION XX . THEOREM . Any two sides of a 40 Pupil - Teacher's Course of Mathematics .
Side 64
... follows : ( 1 ) that each of the equal angles of an isosceles right - angled triangle is half a right angle ; ( 2 ) that each of the three angles of an equilateral triangle is two - thirds of a right angle ; ( 3 ) when two angles of a ...
... follows : ( 1 ) that each of the equal angles of an isosceles right - angled triangle is half a right angle ; ( 2 ) that each of the three angles of an equilateral triangle is two - thirds of a right angle ; ( 3 ) when two angles of a ...
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Euclid, Books I. & II., with Notes, Examples, and Explanations, by a Late ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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 avsnitt
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.