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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Σελίδα 46
... . 8. ) the angles DAC , BAC are equal but ( const . ) DAC is a right angle ; wherefore also BAC is a right angle . Therefore , if the square , & c . : BOOK II . * DEFINITIONS . 1. A RECTANGLE is 46 [ Book I. THE ELEMENTS.
... . 8. ) the angles DAC , BAC are equal but ( const . ) DAC is a right angle ; wherefore also BAC is a right angle . Therefore , if the square , & c . : BOOK II . * DEFINITIONS . 1. A RECTANGLE is 46 [ Book I. THE ELEMENTS.
Σελίδα 47
... RECTANGLE is said to be contained by the two straight lines which are about any of the right angles . † E A H D F K ... rectangle contained by AB and " CD is often expressed simply by AB.CD , a point being placed " between the letters ...
... RECTANGLE is said to be contained by the two straight lines which are about any of the right angles . † E A H D F K ... rectangle contained by AB and " CD is often expressed simply by AB.CD , a point being placed " between the letters ...
Σελίδα 48
... rectangle contained by A and BC is equal to the rectangles contained by A and BD , Á and DE , and A and EC . G B F D EC K LH A From B draw ( I. 11. ) BF at right angles to BC , and ( I. 3. ) make BG equal to A : through G draw ( I. 31 ...
... rectangle contained by A and BC is equal to the rectangles contained by A and BD , Á and DE , and A and EC . G B F D EC K LH A From B draw ( I. 11. ) BF at right angles to BC , and ( I. 3. ) make BG equal to A : through G draw ( I. 31 ...
Σελίδα 49
... rectangle contained by the whole and one of the parts , is equal to the square of that part , together with the rectangle contained by the two parts . Let the straight line AB be divided into two parts in the point C ; the rectangle AB ...
... rectangle contained by the whole and one of the parts , is equal to the square of that part , together with the rectangle contained by the two parts . Let the straight line AB be divided into two parts in the point C ; the rectangle AB ...
Σελίδα 50
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC.CB ; wherefore AG , GE are equal to twice the rectangle AC.CB. The four figures , therefore , HF , CK , AG , GE are equal to the ...
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC.CB ; wherefore AG , GE are equal to twice the rectangle AC.CB. The four figures , therefore , HF , CK , AG , GE are equal to the ...
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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...