The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's Data |
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Page 176
... parallelogram KLMN equal to the excess of EF above C , and similar and similarly situated to D ; but Dis similar to EF , therefore d also KM is similar to EF : Let KL be the homologous side to EG , and LM to 176 THE ELEMENTS.
... parallelogram KLMN equal to the excess of EF above C , and similar and similarly situated to D ; but Dis similar to EF , therefore d also KM is similar to EF : Let KL be the homologous side to EG , and LM to 176 THE ELEMENTS.
Page 177
... excess of the one to be applied above that upon the given line is re- quired to be similar . It is required to apply a parallelogram to the given straight line AB , which shall be equal to the fi- gure C , exceeding by a parallelogram ...
... excess of the one to be applied above that upon the given line is re- quired to be similar . It is required to apply a parallelogram to the given straight line AB , which shall be equal to the fi- gure C , exceeding by a parallelogram ...
Page 210
... excess of the square of AB above the square of XL , and make RX equal to its side , and join RL , RM , RN . Because RX is per- pendicular to the plane of the circle b 3. def . 11. LMN , it is perpendicular to each of the straight lines ...
... excess of the square of AB above the square of XL , and make RX equal to its side , and join RL , RM , RN . Because RX is per- pendicular to the plane of the circle b 3. def . 11. LMN , it is perpendicular to each of the straight lines ...
Page 245
... excess of the circle EFGH , above the space S : Because , by the preceding Lem- ma , if from the greater of two unequal magnitudes there be taken more than its half , and from the remainder more than its half , and so on , there shall ...
... excess of the circle EFGH , above the space S : Because , by the preceding Lem- ma , if from the greater of two unequal magnitudes there be taken more than its half , and from the remainder more than its half , and so on , there shall ...
Page 252
... excess of the pyramid DEFH above the solid Q : Let these , for example , be the pyramids DPRS , STYH : Therefore the prisms which make the rest of the pyramid DEFH , are greater than the solid Q : Divide like- wise the pyramid ABCG in ...
... excess of the pyramid DEFH above the solid Q : Let these , for example , be the pyramids DPRS , STYH : Therefore the prisms which make the rest of the pyramid DEFH , are greater than the solid Q : Divide like- wise the pyramid ABCG in ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABCD 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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 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...
Page 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.
Page 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...
Page 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.