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 Seiten |
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Seite 45
... square , and if BD be joined , the square of BD is equal to the squares of BC , CD , or to those of BA , AC , CD : and thus a square may be found equal to the sum of any number of given squares . Cor . 3. A square may also be found ...
... square , and if BD be joined , the square of BD is equal to the squares of BC , CD , or to those of BA , AC , CD : and thus a square may be found equal to the sum of any number of given squares . Cor . 3. A square may also be found ...
Seite 46
... square of AC is less than the remaining square of DF , and therefore AC is less than DF . PROP . XLVIII . THEOR . IF the square described upon one of the sides of a tri- angle be equal to the squares described upon the other two sides ...
... square of AC is less than the remaining square of DF , and therefore AC is less than DF . PROP . XLVIII . THEOR . IF the square described upon one of the sides of a tri- angle be equal to the squares described upon the other two sides ...
Seite 48
... square of the whole line . Let the straight line AB be divided into any two parts in the point C ; the rectangles AB.AC , and AB.BC are equal to the square of AB . Upon AB describe ( I. 46. ) the square A E , and through C draw ( I. 31 ...
... square of the whole line . Let the straight line AB be divided into any two parts in the point C ; the rectangles AB.AC , and AB.BC are equal to the square of AB . Upon AB describe ( I. 46. ) the square A E , and through C draw ( I. 31 ...
Seite 49
... 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.BC is equal to the square of BC , together with the rectangle AC.CB ...
... 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.BC is equal to the square of BC , together with the rectangle AC.CB ...
Seite 50
... square of AB : therefore the square of AB is equal to the squares of AC , CB , and twice the rectangle AC.CB. Wherefore , & c . Cor . 1. From the demonstration , it is manifest that the paral- lelograms about the diagonal of a square ...
... square of AB : therefore the square of AB is equal to the squares of AC , CB , and twice the rectangle AC.CB. Wherefore , & c . Cor . 1. From the demonstration , it is manifest that the paral- lelograms about the diagonal of a square ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...