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 iv
... apply themselves to Logic without studying in some department of Mathematics ; taking noise and wrangling for proficiency , and thinking refutation accomplished by the instancing of a doubt . This will explain the inscription placed by ...
... apply themselves to Logic without studying in some department of Mathematics ; taking noise and wrangling for proficiency , and thinking refutation accomplished by the instancing of a doubt . This will explain the inscription placed by ...
Σελίδα 37
... apply a parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . Let AB be the given straight line , and C the given triangle , and D the given rectilineal angle . It is ...
... apply a parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . Let AB be the given straight line , and C the given triangle , and D the given rectilineal angle . It is ...
Σελίδα 38
... apply the parallelogram GM equal to the triangle DBC , having the angle GHM equal to the angle E. ( I. 44. ) Then the figure FKML shall be the parallelogram required . Because each of the angles FKH , GHM , is equal to the angle E ...
... apply the parallelogram GM equal to the triangle DBC , having the angle GHM equal to the angle E. ( I. 44. ) Then the figure FKML shall be the parallelogram required . Because each of the angles FKH , GHM , is equal to the angle E ...
Σελίδα 39
... apply a parallelogram , which shall have an angle equal to a given rectilineal angle , and shall be equal to a given rectilineal figure ; viz . by applying to the given straight line a parallelogram equal to the first triangle ABD , ( I ...
... apply a parallelogram , which shall have an angle equal to a given rectilineal angle , and shall be equal to a given rectilineal figure ; viz . by applying to the given straight line a parallelogram equal to the first triangle ABD , ( I ...
Σελίδα 43
... apply to every direction on every side of the line between its extremities . Every straight line situated in a plane , is considered to have two sides ; and when the direction of a line is known , the line is said to be given in ...
... apply to every direction on every side of the line between its extremities . Every straight line situated in a plane , is considered to have two sides ; and when the direction of a line is known , the line is said to be given in ...
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.