Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |
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Αποτελέσματα 6 - 10 από τα 26.
Σελίδα 13
... Demonstration . Let the triangle ABC be taken up , turned round , and put down again with the position of its sides reversed ; • let AB in its new position be named AB ' , and AC in its new position be named AC , Then in the two ...
... Demonstration . Let the triangle ABC be taken up , turned round , and put down again with the position of its sides reversed ; • let AB in its new position be named AB ' , and AC in its new position be named AC , Then in the two ...
Σελίδα 14
... Demonstration . In the triangles AFC , AGB , because AF is equal to AG ( constr . ) , and AC to AB ; ( hyp . ) and the angle A is common to the triangles AFC , AGB ; therefore the base FC is equal to the base GB , ( prop . 4 ) and the ...
... Demonstration . In the triangles AFC , AGB , because AF is equal to AG ( constr . ) , and AC to AB ; ( hyp . ) and the angle A is common to the triangles AFC , AGB ; therefore the base FC is equal to the base GB , ( prop . 4 ) and the ...
Σελίδα 16
... Demonstration . Let the triangle ABC be taken up , turned round , and put down again with its sides reversed ; let B in its new position be named B ′ and C in its new position be named C ' . Place C ' on B , and the line C'B ' on the ...
... Demonstration . Let the triangle ABC be taken up , turned round , and put down again with its sides reversed ; let B in its new position be named B ′ and C in its new position be named C ' . Place C ' on B , and the line C'B ' on the ...
Σελίδα 17
... Demonstration . Then in the triangles DBC , ACB ; because DB is equal to AC , and BC is common to both triangles , and the contained angle DBC is equal to the contained angle ACB , therefore the triangle DBC is equal to the triangle ACB ...
... Demonstration . Then in the triangles DBC , ACB ; because DB is equal to AC , and BC is common to both triangles , and the contained angle DBC is equal to the contained angle ACB , therefore the triangle DBC is equal to the triangle ACB ...
Σελίδα 18
... 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 than the angle BCD , ( ax . 9 ) therefore the angle ADC is ...
... 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 than the angle BCD , ( ax . 9 ) therefore the angle ADC is ...
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.