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 80.
Σελίδα 6
... equal by the eighth definition . Instead of being considered as an axiom , this proposition has been demonstrated by some writers in the following manner : the same plane , so as to make the two 6 [ Book I. THE ELEMENTS.
... equal by the eighth definition . Instead of being considered as an axiom , this proposition has been demonstrated by some writers in the following manner : the same plane , so as to make the two 6 [ Book I. THE ELEMENTS.
Σελίδα 7
... plane , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines shall at length meet upon that side , if they be continually produced . * PROPOSITION I. PROBLEM ...
... plane , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines shall at length meet upon that side , if they be continually produced . * PROPOSITION I. PROBLEM ...
Σελίδα 11
... plane surfaces , which ( I. def . 5. cor . ) is impossible . The triangles are therefore ( I. ax . 8. ) equal . Lastly , since the straight lines BA , BC coincide at the same time with ED , EF , the openings between them must be equal ...
... plane surfaces , which ( I. def . 5. cor . ) is impossible . The triangles are therefore ( I. ax . 8. ) equal . Lastly , since the straight lines BA , BC coincide at the same time with ED , EF , the openings between them must be equal ...
Σελίδα 28
... plane , make the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight * By the fifth corollary to the 32d proposition of this book , if two angles ...
... plane , make the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight * By the fifth corollary to the 32d proposition of this book , if two angles ...
Σελίδα 174
... plane when it makes right angles with all straight lines meeting it in that plane . 2. The inclination of two planes which meet one another , is the angle contained by two straight lines drawn from any point of their common section at ...
... plane when it makes right angles with all straight lines meeting it in that plane . 2. The inclination of two planes which meet one another , is the angle contained by two straight lines drawn from any point of their common section at ...
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...