The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 sider |
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Side 42
... Gnomon . ' parallelogram HG , to- ' gether with the comple- ' ments AF , FC is the A E 6 gnomon , which is more HF G D briefly expressed by the • letters AGK , or EHC , B ' which are at the opposite K C ' angles of the parallelograms ...
... Gnomon . ' parallelogram HG , to- ' gether with the comple- ' ments AF , FC is the A E 6 gnomon , which is more HF G D briefly expressed by the • letters AGK , or EHC , B ' which are at the opposite K C ' angles of the parallelograms ...
Side 46
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : To each of these add LG , which is equal to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the ...
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : To each of these add LG , which is equal to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the ...
Side 47
... gnomon CMG and the figure LG : But the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Wherefore , " if a ...
... gnomon CMG and the figure LG : But the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Wherefore , " if a ...
Side 48
... gnomon AKF , together with the square CK ; therefore the gnomon AKF , together with the square CK , is H double AK : But twice the rect- angle AB , BC is double AK , C c Cor . 4. 2. for BK is equal to BC : There- a 34. 1 . A fore the ...
... gnomon AKF , together with the square CK ; therefore the gnomon AKF , together with the square CK , is H double AK : But twice the rect- angle AB , BC is double AK , C c Cor . 4. 2. for BK is equal to BC : There- a 34. 1 . A fore the ...
Side 49
... gnomon AOH was demonstrated to be quadruple of AK : therefore four times the rectangle AB , BC , is equal to the gnomon AOH . To each of these add XH , which is equal to the square of AC : f Cor . 4. 2 . Therefore four times the ...
... gnomon AOH was demonstrated to be quadruple of AK : therefore four times the rectangle AB , BC , is equal to the gnomon AOH . To each of these add XH , which is equal to the square of AC : f Cor . 4. 2 . Therefore four times the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Ingen forhåndsvisning - 2019 |
Almindelige termer og sætninger
ABC is given altitude angle ABC angle BAC arch base BC BC is equal 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
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Side 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Side 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.
Side 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- 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.
Side 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...
Side 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Side 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.
Side 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Side 28 - 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.
Side 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Side 5 - 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...