The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored : Also, the Book of Euclid's Data, in Like Manner Corrected : to this Edition are Also Annexed, Elements of Plane and Spherical TrigonometryRobert Desilver, 1821 - 516 páginas |
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Página 27
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is great- er than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is great- er than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Página 38
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two A ...
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two A ...
Página 39
... reason , the parallelogram EFGH is equal to the same EBCH : therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
... reason , the parallelogram EFGH is equal to the same EBCH : therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
Página 43
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
Página 47
... reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right an- gle , add to each the angle ABC , and the whole angle DBA is B D L E equal ( 2. Ax . ) to the whole ...
... reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right an- gle , add to each the angle ABC , and the whole angle DBA is B D L E equal ( 2. Ax . ) to the whole ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
AC is equal altitude angle ABC angle BAC base BC BC is given bisected centre circle ABCD circumference cone 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 gnomon greater join less Let ABC meet multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar solid angle solid parallelopipeds sphere spherical angle square of AC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Pasajes populares
Página 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 9 - 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.
Página 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 318 - 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.
Página 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Página 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.