Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Αποτελέσματα 1 - 5 από τα 36.
Σελίδα 13
... reason , and the propriety , of his directing an equilateral triangle to be described upon AB ; and we subjoin these remarks solely for the purpose of pointing out to the student the restrictions which are non - essential to the ...
... reason , and the propriety , of his directing an equilateral triangle to be described upon AB ; and we subjoin these remarks solely for the purpose of pointing out to the student the restrictions which are non - essential to the ...
Σελίδα 26
... the corollary that " the difference of any two sides of a triangle is less than the third side , " and reason as follows : " For , since BA and AC are together PROP . XXI . THEOR . If from the ends 26 YOUNG'S ELEMENTS OF EUCLID ,
... the corollary that " the difference of any two sides of a triangle is less than the third side , " and reason as follows : " For , since BA and AC are together PROP . XXI . THEOR . If from the ends 26 YOUNG'S ELEMENTS OF EUCLID ,
Σελίδα 27
... reason , the exterior angle CEB of the triangle ABE is greater than BAC : and it has been demon- strated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC : and it has been demon- strated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Σελίδα 44
... reason EP is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the whole , or * 2 or 3 Ax . the remainder , AE is equal to the whole or the remainder , DF : AB also is equal † to DC ; there- fore the two EA , AB ...
... reason EP is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the whole , or * 2 or 3 Ax . the remainder , AE is equal to the whole or the remainder , DF : AB also is equal † to DC ; there- fore the two EA , AB ...
Σελίδα 45
... reason , the parallelogram EFGH is equal to the same * Def . 34. 1 . +1 Ax . EBCH : therefore the parallelogram ABCD is equalt to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . Triangles upon the same base ...
... reason , the parallelogram EFGH is equal to the same * Def . 34. 1 . +1 Ax . EBCH : therefore the parallelogram ABCD is equalt to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . Triangles upon the same base ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements [Book 1-6] With Corrections, by J.R. Young Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 105 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Σελίδα 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.