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 100
... multiple of the less . * 3. Magnitudes which can be compared in respect of quantity , that is , which are either ... multiple of a line of 5 inches , containing ít exactly three times ; and a line of 5 inches is a measure , a part , or a ...
... multiple of the less . * 3. Magnitudes which can be compared in respect of quantity , that is , which are either ... multiple of a line of 5 inches , containing ít exactly three times ; and a line of 5 inches is a measure , a part , or a ...
Seite 101
... multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is also greater than the multiple of the fourth , equal to it , or less : then the first of the magnitudes is said to ...
... multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is also greater than the multiple of the fourth , equal to it , or less : then the first of the magnitudes is said to ...
Seite 104
... multiples , are equal to one another . § 3. A multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude of which a multiple is greater than the same multiple of another , is greater than that other ...
... multiples , are equal to one another . § 3. A multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude of which a multiple is greater than the same multiple of another , is greater than that other ...
Seite 105
... multiple AB is of E , the same multiple shall AB and CD together be of E and F together . E G. B H. D F Divide AB into magnitudes equal to E , viz . , AG , GB ; and CD into CH , HD , equal each of them to F : the number therefore , of ...
... multiple AB is of E , the same multiple shall AB and CD together be of E and F together . E G. B H. D F Divide AB into magnitudes equal to E , viz . , AG , GB ; and CD into CH , HD , equal each of them to F : the number therefore , of ...
Seite 106
... multiples EF , GH be taken : then EF is the same multiple of B , that GH is of D. F K + H E A B G C Because EF is the same multiple of A , that GH is of C , there are as many magni- tudes in EF equal to A , as are in GH equal to C ; let ...
... multiples EF , GH be taken : then EF is the same multiple of B , that GH is of D. F K + H E A B G C Because EF is the same multiple of A , that GH is of C , there are as many magni- tudes in EF equal to A , as are in GH equal to C ; let ...
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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
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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...