Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |
Inni boken
Resultat 1-5 av 7
Side 17
... intersect at H , shew ( 1 ) that HF and HG are equal to each other ; ( 2 ) that AH bisects the angle BAC . 3. If G is a point within an equilateral triangle such that the straight lines GA , GB , GC bisect the three angles of the ...
... intersect at H , shew ( 1 ) that HF and HG are equal to each other ; ( 2 ) that AH bisects the angle BAC . 3. If G is a point within an equilateral triangle such that the straight lines GA , GB , GC bisect the three angles of the ...
Side 20
... intersect EF . A B C E D Demonstration . Because in the triangle EDA ' , the side ED is equal to the side EA ' , therefore the angle EDA ' is equal to the angle EA'D : ( prop . 5 ) again , in the triangle FDA ' , since the side FD is ...
... intersect EF . A B C E D Demonstration . Because in the triangle EDA ' , the side ED is equal to the side EA ' , therefore the angle EDA ' is equal to the angle EA'D : ( prop . 5 ) again , in the triangle FDA ' , since the side FD is ...
Side 21
Euclides Thomas Dalton. Secondly . - Let DA ' intersect EF at one of its extremities . A E B Demonstration . Because ... intersect EF produced in some point G. A D F B E G Because the triangle EDA ' is isosceles , therefore the angle EDA ...
Euclides Thomas Dalton. Secondly . - Let DA ' intersect EF at one of its extremities . A E B Demonstration . Because ... intersect EF produced in some point G. A D F B E G Because the triangle EDA ' is isosceles , therefore the angle EDA ...
Side 22
... 3. In the figure of Proposition I. , if F be the other point in which the circles intersect each other , shew that the angle CAF is equal to the angle CBF . 4. If in an equilateral triangle ABC a point G 22 PLANE GEOMETRY .
... 3. In the figure of Proposition I. , if F be the other point in which the circles intersect each other , shew that the angle CAF is equal to the angle CBF . 4. If in an equilateral triangle ABC a point G 22 PLANE GEOMETRY .
Side 27
... intersects AB ; bisect EF in the point G ; ( prop . 10 ) join CE , CG , CF. Then the straight line CG , drawn from C , shall be perpendicular to AB . Demonstration . Because , in the triangles CGE , CGF , EG is equal to FG , ( constr ...
... intersects AB ; bisect EF in the point G ; ( prop . 10 ) join CE , CG , CF. Then the straight line CG , drawn from C , shall be perpendicular to AB . Demonstration . Because , in the triangles CGE , CGF , EG is equal to FG , ( constr ...
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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.