Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 39.
Σελίδα 15
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
Σελίδα 16
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal † to the remaining +3 Ax . angle ACB , which are the angles at the ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal † to the remaining +3 Ax . angle ACB , which are the angles at the ...
Σελίδα 20
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B drawt BE at right angles to AB ; and because ...
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B drawt BE at right angles to AB ; and because ...
Σελίδα 23
... demonstrated that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines cut one another ...
... demonstrated that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines cut one another ...
Σελίδα 24
... demonstrated that the angle BCG , that is , the angle * ACD , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. # 15 . 1 . PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles ...
... demonstrated that the angle BCG , that is , the angle * ACD , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. # 15 . 1 . PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles ...
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.