The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's DataBell & Bradfute, 1835 - 513 Seiten |
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Seite 109
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
Seite 110
... equimultiples of four magnitudes ( taken as in the fifth definition , ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then , the first is ...
... equimultiples of four magnitudes ( taken as in the fifth definition , ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then , the first is ...
Seite 112
... Prop . of Book 5 . AXIOMS . I. EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . 4 Prop . lib . 2. Archimedis de Sphæra et Cylindro . II . Those magnitudes of which the same , or 112 THE ELEMENTS.
... Prop . of Book 5 . AXIOMS . I. EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . 4 Prop . lib . 2. Archimedis de Sphæra et Cylindro . II . Those magnitudes of which the same , or 112 THE ELEMENTS.
Seite 113
... equimultiples , are equal to one another . III . A multiple of a greater magnitude , is greater than the same ... equimultiples of as many others , each of each ; what multiple soever any one of the former magnitudes is of its part , the ...
... equimultiples , are equal to one another . III . A multiple of a greater magnitude , is greater than the same ... equimultiples of as many others , each of each ; what multiple soever any one of the former magnitudes is of its part , the ...
Seite 115
... equimultiples , these will also be equimultiples , the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimul- tiples ...
... equimultiples , these will also be equimultiples , the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimul- tiples ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Keine Leseprobe verfügbar - 2019 |
Häufige Begriffe und Wortgruppen
ABCD altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
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Seite 95 - 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 153 - 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 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Seite 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Seite 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Seite 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Seite 26 - IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite, upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Seite 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.