The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12].1864 |
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Σελίδα 9
... angle BAC is equal to the angle EDF ; therefore also the point C shall coincide with the point F , because AC is equal to DF ; but the point B was shewn to coincide with the point E ; wherefore the base BC shall coincide with the base ...
... angle BAC is equal to the angle EDF ; therefore also the point C shall coincide with the point F , because AC is equal to DF ; but the point B was shewn to coincide with the point E ; wherefore the base BC shall coincide with the base ...
Σελίδα 12
... angle ECD is greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ... BAC shall be equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E ...
... angle ECD is greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ... BAC shall be equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E ...
Σελίδα 13
Euclides Robert Potts. PROPOSITION IX . PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle . It is required to bisect it . A D E F B C In AB take any ...
Euclides Robert Potts. PROPOSITION IX . PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle . It is required to bisect it . A D E F B C In AB take any ...
Σελίδα 20
... angle ACD is equal to the angle ADC ; ( 1. 5. ) but the angle BCD is greater than the angle ACD ; ( ax . 9 ... BAC . B A E D C Produce BD to meet the side AC in E. Because two sides of a triangle are greater than the third side ...
... angle ACD is equal to the angle ADC ; ( 1. 5. ) but the angle BCD is greater than the angle ACD ; ( ax . 9 ... BAC . B A E D C Produce BD to meet the side AC in E. Because two sides of a triangle are greater than the third side ...
Σελίδα 21
... angle BAC ; L.e. Bar and it has been demonstrated , that the angle BDC is greater than the angle CEB ; much more therefore is the angle BDC greater than the angle BAC . Therefore , if from the ends of the side , & c . Q.E.D. PROPOSITION ...
... angle BAC ; L.e. Bar and it has been demonstrated , that the angle BDC is greater than the angle CEB ; much more therefore is the angle BDC greater than the angle BAC . Therefore , if from the ends of the side , & c . Q.E.D. PROPOSITION ...
Άλλες εκδόσεις - Προβολή όλων
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ a₂ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar solid angle square on AC tangent THEOREM third touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Σελίδα 83 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Σελίδα 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Σελίδα 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Σελίδα 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Σελίδα 341 - On the same base, and on the same side of it, there cannot be two triangles...
Σελίδα 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.