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 165
... given straight line simi- lar to one given , and so on . Which was to be done . PROP . XIX . THEOR . Similar triangles are to one another in the dupli- cate ratio of their homologous sides . Let ABC , DEF be similar triangles , having ...
... given straight line simi- lar to one given , and so on . Which was to be done . PROP . XIX . THEOR . Similar triangles are to one another in the dupli- cate ratio of their homologous sides . Let ABC , DEF be similar triangles , having ...
Σελίδα 178
... given rectilineal figure C , exceeding by the parallelogram PO , which is similar to D , because PO is simi- lar to EL 8. Which was to be done . g 24. 6 . PROP . XXX . PROB . To cut a given straight line in extreme and mean ratio . Let ...
... given rectilineal figure C , exceeding by the parallelogram PO , which is similar to D , because PO is simi- lar to EL 8. Which was to be done . g 24. 6 . PROP . XXX . PROB . To cut a given straight line in extreme and mean ratio . Let ...
Σελίδα 299
... proportion of numbers to one another " is defined , and treated of , yet without giving any definition " of the ratio of numbers ; though such a definition was as " necessary and useful to be given in that Book as in this : " But indeed ...
... proportion of numbers to one another " is defined , and treated of , yet without giving any definition " of the ratio of numbers ; though such a definition was as " necessary and useful to be given in that Book as in this : " But indeed ...
Σελίδα 306
... ratio to C ; but they have not . There- " fore A is not equal to B. " The force of which reasoning is this : If A ... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given ...
... ratio to C ; but they have not . There- " fore A is not equal to B. " The force of which reasoning is this : If A ... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given ...
Σελίδα 315
... ratio might have been made after the same manner in which the definitions of duplicate and triplicate ratio are given , viz . " That as in several magnitudes " that are continual proportionals , Euclid named the ratio " of the first to ...
... ratio might have been made after the same manner in which the definitions of duplicate and triplicate ratio are given , viz . " That as in several magnitudes " that are continual proportionals , Euclid named the ratio " of the first to ...
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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.