Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |
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Αποτελέσματα 1 - 5 από τα 6.
Σελίδα 11
... posed upon the other ; if when B is placed upon E , A and BA in the direction of D , it is found that the line BC also falls upon EF , equal . then the angles are BA E Let ABC , DEF be two triangles , in which PROPOSITIONS III . , IV . 11.
... posed upon the other ; if when B is placed upon E , A and BA in the direction of D , it is found that the line BC also falls upon EF , equal . then the angles are BA E Let ABC , DEF be two triangles , in which PROPOSITIONS III . , IV . 11.
Σελίδα 12
... fall upon DF . Again , since AC falls upon DF , and also is equal to it , therefore the point C will coincide with the point F. Now , B coinciding with E , and C with F , the straight line BC will coincide with the straight line EF ...
... fall upon DF . Again , since AC falls upon DF , and also is equal to it , therefore the point C will coincide with the point F. Now , B coinciding with E , and C with F , the straight line BC will coincide with the straight line EF ...
Σελίδα 16
... fall upon BA ; similarly B'A will fall upon СА : therefore the point A will be in its former position : hence C'A ( that is CA ) will exactly coincide with BA , that is CA is equal to BA . Q.E.D. COROLLARY . - Hence every equiangular ...
... fall upon BA ; similarly B'A will fall upon СА : therefore the point A will be in its former position : hence C'A ( that is CA ) will exactly coincide with BA , that is CA is equal to BA . Q.E.D. COROLLARY . - Hence every equiangular ...
Σελίδα 18
... fall without the other . A D B Construction . Join CD . Demonstration . Because in the triangle ACD , the side AC is equal to the side AD , therefore the angle ACD is equal to the angle ADC ; ( prop . 5 ) but the angle ACD is greater ...
... fall without the other . A D B Construction . Join CD . Demonstration . Because in the triangle ACD , the side AC is equal to the side AD , therefore the angle ACD is equal to the angle ADC ; ( prop . 5 ) but the angle ACD is greater ...
Σελίδα 19
... fall on а side of the triangle ACB . D C A B In this case it is evident that AD is not equal to AC . ( ax . 9 ) Therefore in no case can there be two triangles ACB , ADB , on the same side of AB , having the sides AC , AD equal to each ...
... fall on а side of the triangle ACB . D C A B In this case it is evident that AD is not equal to AC . ( ax . 9 ) Therefore in no case can there be two triangles ACB , ADB , on the same side of AB , having the sides AC , AD equal to each ...
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.