Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |
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Side 4
... triangles , are contained by three straight lines . 15. An equilateral triangle has three equal sides . 16. An isosceles triangle has two sides equal . 17. A right - angled triangle is that which has a right angle ; and the side ...
... triangles , are contained by three straight lines . 15. An equilateral triangle has three equal sides . 16. An isosceles triangle has two sides equal . 17. A right - angled triangle is that which has a right angle ; and the side ...
Side 7
... two straight lines being continually produced shall at length meet on that side on which are the angles which are less than two right angles . PROPOSITION I. PROBLEM . To describe an equilateral triangle on POSTULATES AND AXIOMS . t.
... two straight lines being continually produced shall at length meet on that side on which are the angles which are less than two right angles . PROPOSITION I. PROBLEM . To describe an equilateral triangle on POSTULATES AND AXIOMS . t.
Side 8
Euclides Thomas Dalton. PROPOSITION I. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle on AB . A E Construction . With ...
Euclides Thomas Dalton. PROPOSITION I. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle on AB . A E Construction . With ...
Side 9
... equilateral triangle ABD . ( prop . 1 ) Produce the straight lines DA and DB to E and F. ( post . 2 ) With B as centre , at the distance BC , describe the circle CGH , ( post . 3 ) and let G be the point where it meets the straight line ...
... equilateral triangle ABD . ( prop . 1 ) Produce the straight lines DA and DB to E and F. ( post . 2 ) With B as centre , at the distance BC , describe the circle CGH , ( post . 3 ) and let G be the point where it meets the straight line ...
Side 10
... equilateral triangle is described on the other side of the straight line AB . 4. From the middle point of a given straight line draw another straight line of the same length . 5. From the extremity of a given straight line draw a ...
... equilateral triangle is described on the other side of the straight line AB . 4. From the middle point of a given straight line draw another straight line of the same length . 5. From the extremity of a given straight line draw a ...
Andre utgaver - Vis alle
Euclid, Book I., Propositions I. to XXVI., with Exercises and Alternative ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides Ingen forhåndsvisning tilgjengelig - 2023 |
Vanlige uttrykk og setninger
AC is equal ACD is greater angle ABC angle ACB angle BAC angle BCD angle contained angle DEF angle DFE angle EDF angle equal base BC bisects the angle centre circle circumference coincide common constr Construction Demonstration describe the circle distance Divide draw a straight equal angles equal sides equal to CD equidistant equilateral triangle Euclid exterior angle extremities figure Find a point four given point given straight line greater Hence impossible interior intersect isosceles triangle join length less Let ABC likewise line BC meet middle point namely opposite angle opposite sides placed plane position PROBLEM produced proof prop PROPOSITION Prove quadrilateral remainder respects right angles shew shewn side AC sides equal stands taken terminated THEOREM thing triangle ABC triangle DEF triangles be equal unequal whole
Populære avsnitt
Side 39 - IF two triangles have two sides of the one equal to two sides of the...
Side 25 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 4 - 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 7 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 7 - 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 36 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side 37 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Side 18 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Side 29 - 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. At the point B in the straight line AB, let the two straight lines...
Side 3 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.