Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 4 από τα 4.
Σελίδα 7
... whole is greater than its part . 10. Two straight lines cannot inclose a space . 11. All right angles are equal to one another . 12. If a straight line meet two straight lines so as to make the two interior angles on the same side of it ...
... whole is greater than its part . 10. Two straight lines cannot inclose a space . 11. All right angles are equal to one another . 12. If a straight line meet two straight lines so as to make the two interior angles on the same side of it ...
Σελίδα 14
... one to the remaining angles of the other , each to each , to which the equal sides are opposite , namely , the angle ACF to the angle ABG , and the angle AFC to the angle AGB . Again , since the whole AF is equal to the 14 PLANE GEOMETRY .
... one to the remaining angles of the other , each to each , to which the equal sides are opposite , namely , the angle ACF to the angle ABG , and the angle AFC to the angle AGB . Again , since the whole AF is equal to the 14 PLANE GEOMETRY .
Σελίδα 15
... whole angle ABG is equal to the whole angle ACF , and that the parts of these CBG , BCF are also equal , therefore the remaining angle ABC is equal to the remaining angle ACB , ( ax . 3 ) which are the angles at the base of the triangle ...
... whole angle ABG is equal to the whole angle ACF , and that the parts of these CBG , BCF are also equal , therefore the remaining angle ABC is equal to the remaining angle ACB , ( ax . 3 ) which are the angles at the base of the triangle ...
Σελίδα 20
... whole angle EDF is equal to the whole angle EA'F ; ( ax . 2 ) hence the triangles DEF , A'EF must be equal in all respects . ( prop . 4 ) But the triangle A'EF is the triangle ABC in another position , therefore the triangles ABC , DEF ...
... whole angle EDF is equal to the whole angle EA'F ; ( ax . 2 ) hence the triangles DEF , A'EF must be equal in all respects . ( prop . 4 ) But the triangle A'EF is the triangle ABC in another position , therefore the triangles ABC , DEF ...
Άλλες εκδόσεις - Προβολή όλων
Euclid, Book I., Propositions I. to XXVI., with Exercises and Alternative ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 39 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 25 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 37 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.