The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 σελίδες |
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Αποτελέσματα 6 - 10 από τα 74.
Σελίδα 68
... circumference ; ( 1. ) of those which fall upon the concave part of the circumference , the greatest is that which passes through the centre ; and ( 2. ) of the rest , one nearer to the greatest is greater than one more remote . ( 3 ...
... circumference ; ( 1. ) of those which fall upon the concave part of the circumference , the greatest is that which passes through the centre ; and ( 2. ) of the rest , one nearer to the greatest is greater than one more remote . ( 3 ...
Σελίδα 69
... circumference LKG , the least is DG , the external part of DMA ; and a line DK nearer to it is less than DL , one more remote . 1. Join ME , MF , MK , ML ; and because MA is equal to ME , add MD to each ; therefore AD is equal to EM ...
... circumference LKG , the least is DG , the external part of DMA ; and a line DK nearer to it is less than DL , one more remote . 1. Join ME , MF , MK , ML ; and because MA is equal to ME , add MD to each ; therefore AD is equal to EM ...
Σελίδα 73
... circumference in C. Because DAF is a right angle , it is greater ( I. 17. ) than DFA ; and therefore ( I. 19. ) DF is greater than DA . But ( I. def . 30. ) DA is equal to DC ; therefore DF is greater than DC , and the point F is ...
... circumference in C. Because DAF is a right angle , it is greater ( I. 17. ) than DFA ; and therefore ( I. 19. ) DF is greater than DA . But ( I. def . 30. ) DA is equal to DC ; therefore DF is greater than DC , and the point F is ...
Σελίδα 74
... as diameter , as its circumference will cut that of the given circle in the points B and B ' . The reason of this is evident from the 31st proposition of this book . IF For , if not , let F be the 74 [ Book III . THE ELEMENTS.
... as diameter , as its circumference will cut that of the given circle in the points B and B ' . The reason of this is evident from the 31st proposition of this book . IF For , if not , let F be the 74 [ Book III . THE ELEMENTS.
Σελίδα 75
... circumference , upon the same base , that is , upon the same part of the circumference . In the circle ABC , let BEC be an angle at the centre , and BAC an angle at the circumference , which have the same arc BC for their base ; BEC is ...
... circumference , upon the same base , that is , upon the same part of the circumference . In the circle ABC , let BEC be an angle at the centre , and BAC an angle at the circumference , which have the same arc BC for their base ; BEC is ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 53 - 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 at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - 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 on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 32 - 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 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...