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I am not sure about the causative form of する verbs.  
For example, while reading I found this:

> 小源を以て大源に **作用させる** 、魔術師の機械。

I understand this sentence as:

> The mechanism of magicians which let the big source have effect [act]
> through the small one.

So my guess is that it could be rephrased like this.

> 魔術師の機械が小源を以て大源に作用させる

Would the meaning change?

And I have troubles with ようにと.

> 後の世の子孫が、仮に秘奥に“達した”時。その理論を成し得るだけの基礎能力を有する **ようにと** 、何代も重ねて積み上げる“生きた遺産”だ。

My TL:

> In case the future generations whill "reach" those misteries. Making sure
> that they will have the basic power to realize that ideal, it's the
> inheritance accumulated by generations of magicians.

するように=Make sure that  
but  
有するように=Make sure to have [Is this correct?]  
And why is there と at the end?  
Does it stand for と願って、と祈って or such?

Thank you

Edit. I think that a better translation for

> その理論を成し得るだけの基礎能力を有する **ようにと** 、何代も重ねて積み上げる“生きた遺産”だ。

Would be:

> Hoping that they have the basic power to realize [make come true] that
> ideal, it's the inheritance accumulated by generations of magicians.

So ようにと=ようにと願って

Is this right?
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grammar
ようにと meaning and Causative of する verbs
For your first question, I'm not sure what's the "meaning" you refer to. Of
course, they have different grammar, as "the machine of magicians does
something" (a clause) and "the machine of magicians that does something" (a
noun phrase) obviously do, but they indeed depict the same situation.

And for your second question:

**有するようにと**

  * [有する](http://dictionary.goo.ne.jp/jn/224327/meaning/m0u/)  
A verb that means "have", "own", "possess", "embrace" etc., but much more
formal than ordinary "have".  
It's what we call サ変複合動詞, which conjugates in the same way as する.

  * _V_ + ように  
"In order to _V_ "; maybe you memorized it as するように, but remember する is a
placeholder for a verb here.

  * と  
The most basic definition is "that" in "say that" or "think that", but it's
also usable if the verb isn't about verbal expression, in this case it'll
stand as "thinking", "saying", "with the intention of" etc. on its own.  
Actually, this usage is pretty common in Japanese, and we have a bunch of
questions about this "indirect" と on this site, such as:

    * [Embedded question followed by と](https://japanese.stackexchange.com/q/25361/7810)
    * [Question about particle と](https://japanese.stackexchange.com/q/13231/7810)
    * [How does this relative clause work?](https://japanese.stackexchange.com/q/26036/7810)

* * *

Translations:

> 小源を以て大源に作用させる、魔術師の機械。  
>  _A machine of magicians that uses the smaller source to act on the bigger
> source._
>
> 後の世の子孫が、仮に秘奥に“達した”時。その理論を成し得るだけの基礎能力を有するようにと、何代も重ねて積み上げる“生きた遺産”だ。  
>  _It is a "living legacy" to accumulate from generation to generation, in
> order that they_ [=posterity] _will have the basic ability to realize (what
> is in) the theory... if their posterity in the future would ever have
> "attained" the esotery._
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answer