Euclid's Elements of geometry, the first four books, by R. Potts. Corrected and improved1864 |
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Σελίδα
... whole mental system of man ; -to make his speculative inferences coincide with his practical convictions ; -to enable him to render a reason for the belief that is in him , and not to leave him in the con- dition of Solomon's sluggard ...
... whole mental system of man ; -to make his speculative inferences coincide with his practical convictions ; -to enable him to render a reason for the belief that is in him , and not to leave him in the con- dition of Solomon's sluggard ...
Σελίδα 6
... whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior angles on the same side ...
... whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior angles on the same side ...
Σελίδα 9
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it ; also the remaining angles of one triangle coincide with the remain- ing angles of the other , and are equal to them , viz . the angle ABC to the angle DEF ...
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it ; also the remaining angles of one triangle coincide with the remain- ing angles of the other , and are equal to them , viz . the angle ABC to the angle DEF ...
Σελίδα 10
... whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; therefore the remainder BF is equal to the remainder CG ; ( ax . 3. ) and FC has been proved to be equal to GB ; hence , because the two sides BF , FC are ...
... whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; therefore the remainder BF is equal to the remainder CG ; ( ax . 3. ) and FC has been proved to be equal to GB ; hence , because the two sides BF , FC are ...
Σελίδα 29
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC . ( ax . 2. ) Again , because the angle ACD is equal to the two angles ABC , BAC , to each of these equals add the angle ACB , therefore the angles ACD ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC . ( ax . 2. ) Again , because the angle ACD is equal to the two angles ABC , BAC , to each of these equals add the angle ACB , therefore the angles ACD ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry, the First Four Books, by R. Potts. Corrected ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1864 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal Apply Euc axiom base BC bisecting the angle chord circle ABC circumference construction demonstrated describe a circle diagonals diameter double draw equal angles equal to twice equiangular equilateral triangle Euclid Euclid's Elements exterior angle Geometry given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle Let ABC line AC line CD line joining lines be drawn meet the circumference opposite angles opposite sides parallel parallelogram pentagon perpendicular porism problem produced Prop proved quadrilateral figure radius rectangle contained remaining angle right angles right-angled triangle segment semicircle shew shewn side BC square on AC tangent THEOREM touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 118 - 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 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 30 - ... 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.
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 85 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Σελίδα 41 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Σελίδα 126 - EF, that is, AF, is greater than BF : Again, because BE is equal to CE, and FE common to the triangles BEF, CEF, the two sides BE, EF are equal to the two CE, EF; but the angle BEF is greater than the angle CEF ; therefore the base BF is greater (24. 1.) than the base FC ; for the same reason, CF is greater than GF. Again, because GF, FE are greater (20.