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 136
... altitude are one to another as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF have the same altitude , viz . , the perpendicular drawn from the point A to BD then , as the base BC is to the base CD , so is ...
... altitude are one to another as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF have the same altitude , viz . , the perpendicular drawn from the point A to BD then , as the base BC is to the base CD , so is ...
Seite 137
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from the vertices of the triangles to the bases , the straight line which ...
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from the vertices of the triangles to the bases , the straight line which ...
Seite 138
... altitude , viz . , the perpendicular drawn from E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to ADE , so is CE , to EA . Therefore ( V. 11. ) as BD : DA :: CE : EA . 2. Next , let the ...
... altitude , viz . , the perpendicular drawn from E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to ADE , so is CE , to EA . Therefore ( V. 11. ) as BD : DA :: CE : EA . 2. Next , let the ...
Seite 163
... altitude be described , one of them DL , similar to a given parallelogram , the other DF will be the greatest possible , when the segments of the line are equal . PROP . XXVIII . PROB . To divide a given straight line into two parts ...
... altitude be described , one of them DL , similar to a given parallelogram , the other DF will be the greatest possible , when the segments of the line are equal . PROP . XXVIII . PROB . To divide a given straight line into two parts ...
Seite 164
... altitude , is described , equal to the given rectilineal figure K. L H R G K A N V E C But if AH be not equal to K , it is greater by the deter- mination therefore also FG , which ( I. 36. ) is equal to AH , is greater than K. Make ( VI ...
... altitude , is described , equal to the given rectilineal figure K. L H R G K A N V E C But if AH be not equal to K , it is greater by the deter- mination therefore also FG , which ( I. 36. ) is equal to AH , is greater than K. Make ( VI ...
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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...