## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

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Page 67

In analogous or equal Proportion of four Quantities , since the

proportion to the second , as the third has to the fourth ; and consequently , the

In analogous or equal Proportion of four Quantities , since the

**first**has the sameproportion to the second , as the third has to the fourth ; and consequently , the

**first**is to the third as the fecond to fourth ; a Rectangle under the two extreme ... Page 111

As it is the

an Axiom , the Demonftration , being purely mental , is fatisfactory ; though it

fupposes a manual , or mechanical application of one to the other ; the proof

arising ...

As it is the

**first**Proposition on the properties of Figures , which might well pass foran Axiom , the Demonftration , being purely mental , is fatisfactory ; though it

fupposes a manual , or mechanical application of one to the other ; the proof

arising ...

Page 244

fequent ; Def , V. ) But , fince the Consequent of the

Antecedent of the second ( as A : B :: B : C ) three Terms are fuificient to constitute

Analogy ; in which cafe , it is neceflary that they are all of the fame species or ...

fequent ; Def , V. ) But , fince the Consequent of the

**first**Ratia inay , also , be theAntecedent of the second ( as A : B :: B : C ) three Terms are fuificient to constitute

Analogy ; in which cafe , it is neceflary that they are all of the fame species or ...

Page 248

If there be three or more Quantities in one Rank of Order , in any Ratio whatever ,

and as many in another Rank , in the same Ratio , comparing two and wo ; i.e. as

, the

If there be three or more Quantities in one Rank of Order , in any Ratio whatever ,

and as many in another Rank , in the same Ratio , comparing two and wo ; i.e. as

, the

**first**is to the second , in one Rank , so is the**first**to the second , in the ... Page 275

56 : 98 :: 12 : 21 ; which being reduced to their lowest Denomination , the Ratio ,

of each , is determined . The

14 , gives 4 and 7 , the true Ratio of that pair . Now , if the other pair produces the

...

56 : 98 :: 12 : 21 ; which being reduced to their lowest Denomination , the Ratio ,

of each , is determined . The

**first**pair , 56 and 98 , being divided , separately , by14 , gives 4 and 7 , the true Ratio of that pair . Now , if the other pair produces the

...

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A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... Thomas Malton No preview available - 2016 |

### Common terms and phrases

ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe

### Popular passages

Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 221 - 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.

Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.

Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.

Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.

Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.

Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.

Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.