The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 páginas |
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Página 39
... Gnomon . " Thus the parallelogram HG , toge- ther with the complements AF , FC , H F K is the gnomon , which is more briefly expressed by the letters B G C AGK , or EHC , which are at the opposite angles of the pa- rallelograms which ...
... Gnomon . " Thus the parallelogram HG , toge- ther with the complements AF , FC , H F K is the gnomon , which is more briefly expressed by the letters B G C AGK , or EHC , which are at the opposite angles of the pa- rallelograms which ...
Página 43
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : To each of these add LG , which is equal ( п . 4. Cor . ) to the square of CD , therefore the gnomon GMG , together with LG , is equal to the rectangle AD , DB ...
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : To each of these add LG , which is equal ( п . 4. Cor . ) to the square of CD , therefore the gnomon GMG , together with LG , is equal to the rectangle AD , DB ...
Página 44
... 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 . Where- fore , 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 . Where- fore , if a ...
Página 45
... gnomon AOH , are quadruple of AK : And because AK is the rectangle contained by AB , BC , for BK is equal to BC , therefore four times the rectangle AB , BC is qua- druple of AK : But the gnomon AOH was demonstrated to be quadruple ...
... gnomon AOH , are quadruple of AK : And because AK is the rectangle contained by AB , BC , for BK is equal to BC , therefore four times the rectangle AB , BC is qua- druple of AK : But the gnomon AOH was demonstrated to be quadruple ...
Página 46
... gnomon AOH and the square XH : But the gnomon AOH and XH make up the figure AEFD , which is the square of AD : Therefore four times the rectangle AB , BC , together with the square of AC , is equal to the square of AD , that is , of AB ...
... gnomon AOH and the square XH : But the gnomon AOH and XH make up the figure AEFD , which is the square of AD : Therefore four times the rectangle AB , BC , together with the square of AC , is equal to the square of AD , that is , of AB ...
Otras ediciones - Ver todas
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |
Términos y frases comunes
ABCD adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles CAB base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle
Pasajes populares
Página 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 20 - If two triangles have two sides of the one equal to two sides of the...
Página 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Página 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Página 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Página 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 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.
Página 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Página 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.