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 7
... triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . From a given point , to draw a straight line equal to a given straight line . Let A ...
... triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . From a given point , to draw a straight line equal to a given straight line . Let A ...
Σελίδα 9
... triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . A D B C E F For , if the triangle ...
... triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . A D B C E F For , if the triangle ...
Σελίδα 10
... triangle is also equiangular . PROPOSITION VI . THEOREM . If two angles of a triangle be equal to each other ; the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle ...
... triangle is also equiangular . PROPOSITION VI . THEOREM . If two angles of a triangle be equal to each other ; the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle ...
Σελίδα 11
... ABC , because DB is equal to AC , and BC is common to both triangles , the two sides DB , BC are equal to the two ... triangle DBC is equal to the triangle ABC , the less equal to the greater , which is absurd . ( ax . 9. ) Therefore AB ...
... ABC , because DB is equal to AC , and BC is common to both triangles , the two sides DB , BC are equal to the two ... triangle DBC is equal to the triangle ABC , the less equal to the greater , which is absurd . ( ax . 9. ) Therefore AB ...
Σελίδα 12
... triangle ACD , therefore the angles ECD , FDC upon the other side of the ... triangle BCD , therefore the angle BDC is equal to the angle BCD , ( 1. 5. ) but ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ...
... triangle ACD , therefore the angles ECD , FDC upon the other side of the ... triangle BCD , therefore the angle BDC is equal to the angle BCD , ( 1. 5. ) but ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ...
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 - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal 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 BC 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 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.