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 σελίδες |
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Σελίδα 109
... fourth , when any 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 ...
... fourth , when any 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 ...
Σελίδα 110
... fourth . VI . 6 Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying the first is to the second , as the third to the fourth . 6 VII . When of ...
... fourth . VI . 6 Magnitudes which have the same ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying the first is to the second , as the third to the fourth . 6 VII . When of ...
Σελίδα 111
... fourth ; or that the first is to the third , as the second to the fourth : As is shown in the 16th Prop . of this 5th book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
... fourth ; or that the first is to the third , as the second to the fourth : As is shown in the 16th Prop . of this 5th book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
Σελίδα 112
... fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantia , ) or ex æquo , from equality of distance , when there is any number of magnitudes more than two ; and as many others , so that they are proportionals when taken two and ...
... fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantia , ) or ex æquo , from equality of distance , when there is any number of magnitudes more than two ; and as many others , so that they are proportionals when taken two and ...
Σελίδα 114
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . Let AB ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . Let AB ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.