Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |
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Side 32
... shew that BDC is an obtuse angle . 4. From any point outside a straight line two equal straight lines can be drawn to ... shewn that the angles BAC , ACB are together less than two right angles , and also the angles BAC , ABC . Q.F.D. ...
... shew that BDC is an obtuse angle . 4. From any point outside a straight line two equal straight lines can be drawn to ... shewn that the angles BAC , ACB are together less than two right angles , and also the angles BAC , ABC . Q.F.D. ...
Side 35
... shewn that AB , BC are greater than AC , and AC , CB greater than AB . Exercises . Q.E.D. 1. Construct the figure so as to prove ( 1 ) that AB , BC are greater than AC , and ( 2 ) that AC , CB are greater than AB . 2. Prove the ...
... shewn that AB , BC are greater than AC , and AC , CB greater than AB . Exercises . Q.E.D. 1. Construct the figure so as to prove ( 1 ) that AB , BC are greater than AC , and ( 2 ) that AC , CB are greater than AB . 2. Prove the ...
Side 39
... ( prop . 19 ) therefore the side EG is greater than the side EF . But it has been shewn that BC is equal to EG ; therefore also BC is greater than EF . Q.E.D. Exercises . 1. Why is it necessary to state in PROPOSITION ΧΧΙΡ . 39.
... ( prop . 19 ) therefore the side EG is greater than the side EF . But it has been shewn that BC is equal to EG ; therefore also BC is greater than EF . Q.E.D. Exercises . 1. Why is it necessary to state in PROPOSITION ΧΧΙΡ . 39.
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Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides Ingen forhåndsvisning tilgjengelig - 2023 |
Vanlige uttrykk og setninger
A'EF AB is equal AC is equal ACD is greater adjacent angles angle ABC angle ACB angle BAC angle BCD angle BDC greater angle contained angle DEF angle DFE angle EDF angle equal bisects the angle centre circumference constr DEF are equal Demonstration describe the circle draw a straight equal angles equal sides equal to CD equidistant equilateral triangle Euclid exterior angle Find a point four-sided figure given line given point given straight line greater than BC interior opposite angle intersect isosceles triangle less Let ABC line with BC middle point opposite sides perpendiculars let fall point G position be named produced prop PROPOSITION Q.E.D. Exercises quadrilateral right angles shew shewn side AC sides equal straight line drawn take any point THEOREM third side triangle ABC triangle DEF triangles be equal unequal vertical angle
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.